id	sid	tid	token	lemma	pos
ejpam-6985	1	1	european	european	PROPN
ejpam-6985	1	2	journal	journal	PROPN
ejpam-6985	1	3	of	of	ADP
ejpam-6985	1	4	pure	pure	ADJ
ejpam-6985	1	5	and	and	CCONJ
ejpam-6985	1	6	applied	applied	ADJ
ejpam-6985	1	7	mathematics	mathematic	NOUN
ejpam-6985	1	8	2025	2025	NUM
ejpam-6985	1	9	,	,	PUNCT
ejpam-6985	1	10	vol	vol	NOUN
ejpam-6985	1	11	.	.	PROPN
ejpam-6985	1	12	18	18	NUM
ejpam-6985	1	13	,	,	PUNCT
ejpam-6985	1	14	issue	issue	NOUN
ejpam-6985	1	15	4	4	NUM
ejpam-6985	1	16	,	,	PUNCT
ejpam-6985	1	17	article	article	NOUN
ejpam-6985	1	18	number	number	NOUN
ejpam-6985	1	19	6985	6985	NUM
ejpam-6985	1	20	issn	issn	PROPN
ejpam-6985	1	21	1307	1307	NUM
ejpam-6985	1	22	-	-	SYM
ejpam-6985	1	23	5543	5543	NUM
ejpam-6985	1	24	–	–	PUNCT
ejpam-6985	1	25	ejpam.com	ejpam.com	X
ejpam-6985	1	26	published	publish	VERB
ejpam-6985	1	27	by	by	ADP
ejpam-6985	1	28	new	new	PROPN
ejpam-6985	1	29	york	york	PROPN
ejpam-6985	1	30	business	business	PROPN
ejpam-6985	1	31	global	global	PROPN
ejpam-6985	1	32	a	a	DET
ejpam-6985	1	33	cheeger	cheeger	ADJ
ejpam-6985	1	34	-	-	PUNCT
ejpam-6985	1	35	type	type	NOUN
ejpam-6985	1	36	inequality	inequality	NOUN
ejpam-6985	1	37	for	for	ADP
ejpam-6985	1	38	the	the	DET
ejpam-6985	1	39	sub	sub	NOUN
ejpam-6985	1	40	-	-	NOUN
ejpam-6985	1	41	laplacian	laplacian	ADJ
ejpam-6985	1	42	on	on	ADP
ejpam-6985	1	43	pseudo	pseudo	NOUN
ejpam-6985	1	44	-	-	ADJ
ejpam-6985	1	45	hermitian	hermitian	ADJ
ejpam-6985	1	46	cr	cr	PROPN
ejpam-6985	1	47	manifolds	manifolds	PROPN
ejpam-6985	1	48	ali	ali	PROPN
ejpam-6985	1	49	ben	ben	PROPN
ejpam-6985	1	50	ahmed	ahmed	PROPN
ejpam-6985	1	51	department	department	PROPN
ejpam-6985	1	52	of	of	ADP
ejpam-6985	1	53	mathematics	mathematics	PROPN
ejpam-6985	1	54	,	,	PUNCT
ejpam-6985	1	55	university	university	NOUN
ejpam-6985	1	56	college	college	PROPN
ejpam-6985	1	57	al	al	PROPN
ejpam-6985	1	58	-	-	PUNCT
ejpam-6985	1	59	khafji	khafji	PROPN
ejpam-6985	1	60	,	,	PUNCT
ejpam-6985	1	61	university	university	NOUN
ejpam-6985	1	62	of	of	ADP
ejpam-6985	1	63	hafr	hafr	PROPN
ejpam-6985	1	64	al	al	PROPN
ejpam-6985	1	65	batin	batin	PROPN
ejpam-6985	1	66	,	,	PUNCT
ejpam-6985	1	67	saudi	saudi	PROPN
ejpam-6985	1	68	arabia	arabia	PROPN
ejpam-6985	1	69	abstract	abstract	NOUN
ejpam-6985	1	70	.	.	PUNCT
ejpam-6985	2	1	in	in	ADP
ejpam-6985	2	2	this	this	DET
ejpam-6985	2	3	paper	paper	NOUN
ejpam-6985	2	4	,	,	PUNCT
ejpam-6985	2	5	we	we	PRON
ejpam-6985	2	6	introduce	introduce	VERB
ejpam-6985	2	7	a	a	DET
ejpam-6985	2	8	cr	cr	X
ejpam-6985	2	9	cheeger	cheeger	ADV
ejpam-6985	2	10	constant	constant	ADJ
ejpam-6985	2	11	and	and	CCONJ
ejpam-6985	2	12	establish	establish	VERB
ejpam-6985	2	13	cheeger	cheeger	ADJ
ejpam-6985	2	14	-	-	PUNCT
ejpam-6985	2	15	type	type	NOUN
ejpam-6985	2	16	and	and	CCONJ
ejpam-6985	2	17	buser	buser	NOUN
ejpam-6985	2	18	-	-	PUNCT
ejpam-6985	2	19	type	type	NOUN
ejpam-6985	2	20	inequalities	inequality	NOUN
ejpam-6985	2	21	for	for	ADP
ejpam-6985	2	22	the	the	DET
ejpam-6985	2	23	first	first	ADJ
ejpam-6985	2	24	nonzero	nonzero	NOUN
ejpam-6985	2	25	eigenvalue	eigenvalue	NOUN
ejpam-6985	2	26	of	of	ADP
ejpam-6985	2	27	the	the	DET
ejpam-6985	2	28	sub	sub	NOUN
ejpam-6985	2	29	-	-	NOUN
ejpam-6985	2	30	laplacian	laplacian	ADJ
ejpam-6985	2	31	on	on	ADP
ejpam-6985	2	32	compact	compact	ADJ
ejpam-6985	2	33	strictly	strictly	ADV
ejpam-6985	2	34	pseudoconvex	pseudoconvex	VERB
ejpam-6985	2	35	pseudo	pseudo	NOUN
ejpam-6985	2	36	-	-	ADJ
ejpam-6985	2	37	hermitian	hermitian	ADJ
ejpam-6985	2	38	cr	cr	PROPN
ejpam-6985	2	39	manifolds	manifolds	PROPN
ejpam-6985	2	40	.	.	PUNCT
ejpam-6985	3	1	these	these	DET
ejpam-6985	3	2	results	result	NOUN
ejpam-6985	3	3	extend	extend	VERB
ejpam-6985	3	4	classical	classical	ADJ
ejpam-6985	3	5	isoperimetric	isoperimetric	ADJ
ejpam-6985	3	6	bounds	bound	NOUN
ejpam-6985	3	7	from	from	ADP
ejpam-6985	3	8	riemannian	riemannian	NOUN
ejpam-6985	3	9	to	to	ADP
ejpam-6985	3	10	cr	cr	PROPN
ejpam-6985	3	11	geometry	geometry	PROPN
ejpam-6985	3	12	.	.	PUNCT
ejpam-6985	4	1	applications	application	NOUN
ejpam-6985	4	2	are	be	AUX
ejpam-6985	4	3	given	give	VERB
ejpam-6985	4	4	to	to	AUX
ejpam-6985	4	5	model	model	VERB
ejpam-6985	4	6	examples	example	NOUN
ejpam-6985	4	7	,	,	PUNCT
ejpam-6985	4	8	including	include	VERB
ejpam-6985	4	9	the	the	DET
ejpam-6985	4	10	heisenberg	heisenberg	PROPN
ejpam-6985	4	11	quotients	quotient	NOUN
ejpam-6985	4	12	,	,	PUNCT
ejpam-6985	4	13	the	the	DET
ejpam-6985	4	14	standard	standard	NOUN
ejpam-6985	4	15	cr	cr	PRON
ejpam-6985	4	16	sphere	sphere	ADV
ejpam-6985	4	17	and	and	CCONJ
ejpam-6985	4	18	rossi	rossi	VERB
ejpam-6985	4	19	’s	’s	PART
ejpam-6985	4	20	non	non	ADJ
ejpam-6985	4	21	-	-	ADJ
ejpam-6985	4	22	embeddable	embeddable	ADJ
ejpam-6985	4	23	deformations	deformation	NOUN
ejpam-6985	4	24	.	.	PUNCT
ejpam-6985	5	1	2020	2020	NUM
ejpam-6985	5	2	mathematics	mathematic	NOUN
ejpam-6985	5	3	subject	subject	NOUN
ejpam-6985	5	4	classifications	classification	NOUN
ejpam-6985	5	5	:	:	PUNCT
ejpam-6985	5	6	32v05	32v05	NUM
ejpam-6985	5	7	,	,	PUNCT
ejpam-6985	5	8	53c17	53c17	NUM
ejpam-6985	5	9	,	,	PUNCT
ejpam-6985	5	10	58j50	58j50	NUM
ejpam-6985	5	11	key	key	ADJ
ejpam-6985	5	12	words	word	NOUN
ejpam-6985	5	13	and	and	CCONJ
ejpam-6985	5	14	phrases	phrase	NOUN
ejpam-6985	5	15	:	:	PUNCT
ejpam-6985	5	16	cr	cr	PROPN
ejpam-6985	5	17	manifolds	manifold	NOUN
ejpam-6985	5	18	,	,	PUNCT
ejpam-6985	5	19	sub	sub	ADJ
ejpam-6985	5	20	-	-	ADJ
ejpam-6985	5	21	laplacian	laplacian	ADJ
ejpam-6985	5	22	,	,	PUNCT
ejpam-6985	5	23	cheeger	cheeger	ADJ
ejpam-6985	5	24	inequality	inequality	NOUN
ejpam-6985	5	25	,	,	PUNCT
ejpam-6985	5	26	isoperimetric	isoperimetric	ADJ
ejpam-6985	5	27	constant	constant	ADJ
ejpam-6985	5	28	1	1	NUM
ejpam-6985	5	29	.	.	PUNCT
ejpam-6985	5	30	introduction	introduction	NOUN
ejpam-6985	5	31	the	the	DET
ejpam-6985	5	32	discovery	discovery	NOUN
ejpam-6985	5	33	of	of	ADP
ejpam-6985	5	34	cheeger	cheeger	PROPN
ejpam-6985	5	35	’s	’s	PART
ejpam-6985	5	36	inequality	inequality	NOUN
ejpam-6985	5	37	in	in	ADP
ejpam-6985	5	38	1970	1970	NUM
ejpam-6985	6	1	[	[	X
ejpam-6985	6	2	1	1	X
ejpam-6985	6	3	]	]	PUNCT
ejpam-6985	6	4	marked	mark	VERB
ejpam-6985	6	5	a	a	DET
ejpam-6985	6	6	turning	turning	NOUN
ejpam-6985	6	7	point	point	NOUN
ejpam-6985	6	8	in	in	ADP
ejpam-6985	6	9	geometric	geometric	ADJ
ejpam-6985	6	10	analysis	analysis	NOUN
ejpam-6985	6	11	,	,	PUNCT
ejpam-6985	6	12	establishing	establish	VERB
ejpam-6985	6	13	a	a	DET
ejpam-6985	6	14	precise	precise	ADJ
ejpam-6985	6	15	link	link	NOUN
ejpam-6985	6	16	between	between	ADP
ejpam-6985	6	17	isoperimetric	isoperimetric	ADJ
ejpam-6985	6	18	geometry	geometry	NOUN
ejpam-6985	6	19	and	and	CCONJ
ejpam-6985	6	20	spectral	spectral	ADJ
ejpam-6985	6	21	theory	theory	NOUN
ejpam-6985	6	22	.	.	PUNCT
ejpam-6985	7	1	for	for	ADP
ejpam-6985	7	2	a	a	DET
ejpam-6985	7	3	compact	compact	ADJ
ejpam-6985	7	4	riemannian	riemannian	NOUN
ejpam-6985	7	5	manifold	manifold	NOUN
ejpam-6985	7	6	(	(	PUNCT
ejpam-6985	7	7	m	m	PROPN
ejpam-6985	7	8	,	,	PUNCT
ejpam-6985	7	9	g	g	NOUN
ejpam-6985	7	10	)	)	PUNCT
ejpam-6985	7	11	without	without	ADP
ejpam-6985	7	12	boundary	boundary	NOUN
ejpam-6985	7	13	,	,	PUNCT
ejpam-6985	7	14	cheeger	cheeger	NOUN
ejpam-6985	7	15	showed	show	VERB
ejpam-6985	7	16	that	that	SCONJ
ejpam-6985	7	17	the	the	DET
ejpam-6985	7	18	first	first	ADJ
ejpam-6985	7	19	nonzero	nonzero	PROPN
ejpam-6985	7	20	eigenvalue	eigenvalue	PROPN
ejpam-6985	7	21	λ1(∆g	λ1(∆g	PROPN
ejpam-6985	7	22	)	)	PUNCT
ejpam-6985	7	23	of	of	ADP
ejpam-6985	7	24	the	the	DET
ejpam-6985	7	25	laplace	laplace	NOUN
ejpam-6985	7	26	–	–	PUNCT
ejpam-6985	7	27	beltrami	beltrami	ADJ
ejpam-6985	7	28	operator	operator	NOUN
ejpam-6985	7	29	∆g	∆g	PROPN
ejpam-6985	7	30	satisfies	satisfie	NOUN
ejpam-6985	7	31	λ1(∆g	λ1(∆g	PROPN
ejpam-6985	7	32	)	)	PUNCT
ejpam-6985	7	33	≥	≥	NOUN
ejpam-6985	7	34	1	1	NUM
ejpam-6985	7	35	4	4	NUM
ejpam-6985	7	36	h(m)2	h(m)2	PROPN
ejpam-6985	7	37	,	,	PUNCT
ejpam-6985	7	38	(	(	PUNCT
ejpam-6985	7	39	1.1	1.1	NUM
ejpam-6985	7	40	)	)	PUNCT
ejpam-6985	7	41	where	where	SCONJ
ejpam-6985	7	42	h(m	h(m	NOUN
ejpam-6985	7	43	)	)	PUNCT
ejpam-6985	7	44	is	be	AUX
ejpam-6985	7	45	the	the	DET
ejpam-6985	7	46	isoperimetric	isoperimetric	ADJ
ejpam-6985	7	47	constant	constant	ADJ
ejpam-6985	7	48	.	.	PUNCT
ejpam-6985	8	1	this	this	DET
ejpam-6985	8	2	inequality	inequality	NOUN
ejpam-6985	8	3	has	have	AUX
ejpam-6985	8	4	had	have	VERB
ejpam-6985	8	5	far	far	ADV
ejpam-6985	8	6	-	-	PUNCT
ejpam-6985	8	7	reaching	reach	VERB
ejpam-6985	8	8	consequences	consequence	NOUN
ejpam-6985	8	9	,	,	PUNCT
ejpam-6985	8	10	providing	provide	VERB
ejpam-6985	8	11	a	a	DET
ejpam-6985	8	12	bridge	bridge	NOUN
ejpam-6985	8	13	between	between	ADP
ejpam-6985	8	14	geometry	geometry	NOUN
ejpam-6985	8	15	and	and	CCONJ
ejpam-6985	8	16	analysis	analysis	NOUN
ejpam-6985	8	17	through	through	ADP
ejpam-6985	8	18	applications	application	NOUN
ejpam-6985	8	19	to	to	ADP
ejpam-6985	8	20	sobolev	sobolev	NOUN
ejpam-6985	8	21	inequalities	inequality	NOUN
ejpam-6985	8	22	,	,	PUNCT
ejpam-6985	8	23	heat	heat	NOUN
ejpam-6985	8	24	kernel	kernel	NOUN
ejpam-6985	8	25	bounds	bound	NOUN
ejpam-6985	8	26	and	and	CCONJ
ejpam-6985	8	27	concentration	concentration	NOUN
ejpam-6985	8	28	phenomena	phenomenon	NOUN
ejpam-6985	8	29	.	.	PUNCT
ejpam-6985	9	1	a	a	DET
ejpam-6985	9	2	decade	decade	NOUN
ejpam-6985	9	3	later	later	ADV
ejpam-6985	9	4	,	,	PUNCT
ejpam-6985	9	5	buser	buser	NOUN
ejpam-6985	9	6	[	[	X
ejpam-6985	9	7	2	2	NUM
ejpam-6985	9	8	]	]	X
ejpam-6985	9	9	complemented	complement	VERB
ejpam-6985	9	10	cheeger	cheeger	ADJ
ejpam-6985	9	11	’s	’s	PART
ejpam-6985	9	12	estimate	estimate	NOUN
ejpam-6985	9	13	with	with	ADP
ejpam-6985	9	14	an	an	DET
ejpam-6985	9	15	upper	upper	ADJ
ejpam-6985	9	16	bound	bind	VERB
ejpam-6985	9	17	depending	depend	VERB
ejpam-6985	9	18	on	on	ADP
ejpam-6985	9	19	curvature	curvature	NOUN
ejpam-6985	9	20	,	,	PUNCT
ejpam-6985	9	21	thereby	thereby	ADV
ejpam-6985	9	22	giving	give	VERB
ejpam-6985	9	23	a	a	DET
ejpam-6985	9	24	two	two	NUM
ejpam-6985	9	25	-	-	PUNCT
ejpam-6985	9	26	sided	sided	ADJ
ejpam-6985	9	27	description	description	NOUN
ejpam-6985	9	28	of	of	ADP
ejpam-6985	9	29	the	the	DET
ejpam-6985	9	30	spectral	spectral	ADJ
ejpam-6985	9	31	gap	gap	NOUN
ejpam-6985	9	32	in	in	ADP
ejpam-6985	9	33	terms	term	NOUN
ejpam-6985	9	34	of	of	ADP
ejpam-6985	9	35	isoperimetry	isoperimetry	NOUN
ejpam-6985	9	36	.	.	PUNCT
ejpam-6985	10	1	the	the	DET
ejpam-6985	10	2	present	present	ADJ
ejpam-6985	10	3	work	work	NOUN
ejpam-6985	10	4	develops	develop	VERB
ejpam-6985	10	5	this	this	DET
ejpam-6985	10	6	classical	classical	ADJ
ejpam-6985	10	7	picture	picture	NOUN
ejpam-6985	10	8	in	in	ADP
ejpam-6985	10	9	the	the	DET
ejpam-6985	10	10	strictly	strictly	ADV
ejpam-6985	10	11	pseudoconvex	pseudoconvex	PROPN
ejpam-6985	10	12	cr	cr	PROPN
ejpam-6985	10	13	manifolds	manifolds	PROPN
ejpam-6985	10	14	.	.	PUNCT
ejpam-6985	11	1	here	here	ADV
ejpam-6985	11	2	the	the	DET
ejpam-6985	11	3	natural	natural	ADJ
ejpam-6985	11	4	second	second	ADJ
ejpam-6985	11	5	-	-	PUNCT
ejpam-6985	11	6	order	order	NOUN
ejpam-6985	11	7	operator	operator	NOUN
ejpam-6985	11	8	is	be	AUX
ejpam-6985	11	9	the	the	DET
ejpam-6985	11	10	horizontal	horizontal	ADJ
ejpam-6985	11	11	sub	sub	ADJ
ejpam-6985	11	12	-	-	ADJ
ejpam-6985	11	13	laplacian	laplacian	ADJ
ejpam-6985	11	14	∆b	∆b	PROPN
ejpam-6985	11	15	,	,	PUNCT
ejpam-6985	11	16	acting	act	VERB
ejpam-6985	11	17	along	along	ADP
ejpam-6985	11	18	the	the	DET
ejpam-6985	11	19	contact	contact	NOUN
ejpam-6985	11	20	distribution	distribution	NOUN
ejpam-6985	11	21	determined	determine	VERB
ejpam-6985	11	22	by	by	ADP
ejpam-6985	11	23	a	a	DET
ejpam-6985	11	24	pseudo	pseudo	NOUN
ejpam-6985	11	25	-	-	ADJ
ejpam-6985	11	26	hermitian	hermitian	ADJ
ejpam-6985	11	27	structure	structure	NOUN
ejpam-6985	11	28	.	.	PUNCT
ejpam-6985	12	1	extending	extend	VERB
ejpam-6985	12	2	cheeger	cheeger	ADJ
ejpam-6985	12	3	’s	’s	PART
ejpam-6985	12	4	method	method	NOUN
ejpam-6985	12	5	from	from	ADP
ejpam-6985	12	6	the	the	DET
ejpam-6985	12	7	elliptic	elliptic	ADJ
ejpam-6985	12	8	to	to	ADP
ejpam-6985	12	9	the	the	DET
ejpam-6985	12	10	hypoelliptic	hypoelliptic	ADJ
ejpam-6985	12	11	world	world	NOUN
ejpam-6985	12	12	presents	present	VERB
ejpam-6985	12	13	several	several	ADJ
ejpam-6985	12	14	difficulties	difficulty	NOUN
ejpam-6985	12	15	:	:	PUNCT
ejpam-6985	12	16	doi	doi	NOUN
ejpam-6985	12	17	:	:	PUNCT
ejpam-6985	12	18	https://doi.org/10.29020/nybg.ejpam.v18i4.6985	https://doi.org/10.29020/nybg.ejpam.v18i4.6985	X
ejpam-6985	12	19	email	email	NOUN
ejpam-6985	12	20	address	address	NOUN
ejpam-6985	12	21	:	:	PUNCT
ejpam-6985	12	22	benahmedal@gmail.com	benahmedal@gmail.com	X
ejpam-6985	13	1	(	(	PUNCT
ejpam-6985	13	2	a.	a.	PROPN
ejpam-6985	13	3	ben	ben	PROPN
ejpam-6985	13	4	ahmed	ahmed	PROPN
ejpam-6985	13	5	)	)	PUNCT
ejpam-6985	13	6	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6985	14	1	1	1	NUM
ejpam-6985	14	2	copyright	copyright	NOUN
ejpam-6985	14	3	:	:	PUNCT
ejpam-6985	14	4	©	©	PROPN
ejpam-6985	14	5	2025	2025	NUM
ejpam-6985	14	6	the	the	DET
ejpam-6985	14	7	author(s	author(s	NOUN
ejpam-6985	14	8	)	)	PUNCT
ejpam-6985	14	9	.	.	PUNCT
ejpam-6985	15	1	(	(	PUNCT
ejpam-6985	15	2	cc	cc	NOUN
ejpam-6985	15	3	by	by	ADP
ejpam-6985	15	4	-	-	PUNCT
ejpam-6985	15	5	nc	nc	PROPN
ejpam-6985	15	6	4.0	4.0	NUM
ejpam-6985	15	7	)	)	PUNCT
ejpam-6985	15	8	a.	a.	NOUN
ejpam-6985	15	9	ben	ben	PROPN
ejpam-6985	15	10	ahmed	ahmed	PROPN
ejpam-6985	15	11	/	/	SYM
ejpam-6985	15	12	eur	eur	PROPN
ejpam-6985	15	13	.	.	PUNCT
ejpam-6985	16	1	j.	j.	PROPN
ejpam-6985	16	2	pure	pure	PROPN
ejpam-6985	16	3	appl	appl	PROPN
ejpam-6985	16	4	.	.	PROPN
ejpam-6985	16	5	math	math	PROPN
ejpam-6985	16	6	,	,	PUNCT
ejpam-6985	16	7	18	18	NUM
ejpam-6985	16	8	(	(	PUNCT
ejpam-6985	16	9	4	4	NUM
ejpam-6985	16	10	)	)	PUNCT
ejpam-6985	16	11	(	(	PUNCT
ejpam-6985	16	12	2025	2025	NUM
ejpam-6985	16	13	)	)	PUNCT
ejpam-6985	16	14	,	,	PUNCT
ejpam-6985	16	15	6985	6985	NUM
ejpam-6985	16	16	2	2	NUM
ejpam-6985	16	17	of	of	ADP
ejpam-6985	16	18	16	16	NUM
ejpam-6985	16	19	the	the	DET
ejpam-6985	16	20	horizontal	horizontal	ADJ
ejpam-6985	16	21	bundle	bundle	NOUN
ejpam-6985	16	22	exhibits	exhibit	VERB
ejpam-6985	16	23	anisotropic	anisotropic	NOUN
ejpam-6985	16	24	scaling	scaling	NOUN
ejpam-6985	16	25	,	,	PUNCT
ejpam-6985	16	26	notions	notion	NOUN
ejpam-6985	16	27	of	of	ADP
ejpam-6985	16	28	perimeter	perimeter	NOUN
ejpam-6985	16	29	must	must	AUX
ejpam-6985	16	30	be	be	AUX
ejpam-6985	16	31	recast	recast	VERB
ejpam-6985	16	32	using	use	VERB
ejpam-6985	16	33	horizontal	horizontal	ADJ
ejpam-6985	16	34	bv	bv	PROPN
ejpam-6985	16	35	theory	theory	NOUN
ejpam-6985	16	36	and	and	CCONJ
ejpam-6985	16	37	torsion	torsion	NOUN
ejpam-6985	16	38	terms	term	NOUN
ejpam-6985	16	39	arising	arise	VERB
ejpam-6985	16	40	from	from	ADP
ejpam-6985	16	41	the	the	DET
ejpam-6985	16	42	tanaka	tanaka	NOUN
ejpam-6985	16	43	–	–	PUNCT
ejpam-6985	16	44	webster	webster	PROPN
ejpam-6985	16	45	connection	connection	NOUN
ejpam-6985	16	46	affect	affect	VERB
ejpam-6985	16	47	the	the	DET
ejpam-6985	16	48	analytic	analytic	ADJ
ejpam-6985	16	49	inequalities	inequality	NOUN
ejpam-6985	16	50	.	.	PUNCT
ejpam-6985	17	1	these	these	DET
ejpam-6985	17	2	challenges	challenge	NOUN
ejpam-6985	17	3	motivated	motivate	VERB
ejpam-6985	17	4	the	the	DET
ejpam-6985	17	5	development	development	NOUN
ejpam-6985	17	6	of	of	ADP
ejpam-6985	17	7	horizontal	horizontal	ADJ
ejpam-6985	17	8	analysis	analysis	NOUN
ejpam-6985	17	9	in	in	ADP
ejpam-6985	17	10	carnot	carnot	NOUN
ejpam-6985	17	11	–	–	PUNCT
ejpam-6985	17	12	carathéodory	carathéodory	NOUN
ejpam-6985	17	13	spaces	space	NOUN
ejpam-6985	17	14	,	,	PUNCT
ejpam-6985	17	15	most	most	ADV
ejpam-6985	17	16	notably	notably	ADV
ejpam-6985	17	17	by	by	ADP
ejpam-6985	17	18	folland	folland	NOUN
ejpam-6985	17	19	and	and	CCONJ
ejpam-6985	17	20	stein	stein	PROPN
ejpam-6985	18	1	[	[	X
ejpam-6985	18	2	3	3	NUM
ejpam-6985	18	3	]	]	PUNCT
ejpam-6985	18	4	,	,	PUNCT
ejpam-6985	18	5	jerison	jerison	PROPN
ejpam-6985	18	6	and	and	CCONJ
ejpam-6985	18	7	lee	lee	PROPN
ejpam-6985	18	8	in	in	ADP
ejpam-6985	18	9	their	their	PRON
ejpam-6985	18	10	study	study	NOUN
ejpam-6985	18	11	of	of	ADP
ejpam-6985	18	12	the	the	DET
ejpam-6985	18	13	cr	cr	PROPN
ejpam-6985	18	14	yamabe	yamabe	PROPN
ejpam-6985	18	15	problem	problem	NOUN
ejpam-6985	19	1	[	[	X
ejpam-6985	19	2	4	4	NUM
ejpam-6985	19	3	,	,	PUNCT
ejpam-6985	19	4	5	5	NUM
ejpam-6985	19	5	]	]	PUNCT
ejpam-6985	19	6	and	and	CCONJ
ejpam-6985	19	7	franchi	franchi	PROPN
ejpam-6985	19	8	–	–	PUNCT
ejpam-6985	19	9	serapioni	serapioni	NOUN
ejpam-6985	19	10	–	–	PUNCT
ejpam-6985	19	11	serra	serra	PROPN
ejpam-6985	19	12	cassano	cassano	PROPN
ejpam-6985	19	13	and	and	CCONJ
ejpam-6985	19	14	garofalo	garofalo	PROPN
ejpam-6985	19	15	–	–	PUNCT
ejpam-6985	19	16	nhieu	nhieu	NOUN
ejpam-6985	20	1	[	[	X
ejpam-6985	20	2	6	6	NUM
ejpam-6985	20	3	,	,	PUNCT
ejpam-6985	20	4	7	7	NUM
ejpam-6985	20	5	]	]	PUNCT
ejpam-6985	20	6	,	,	PUNCT
ejpam-6985	20	7	who	who	PRON
ejpam-6985	20	8	introduced	introduce	VERB
ejpam-6985	20	9	horizontal	horizontal	ADJ
ejpam-6985	20	10	bv	bv	PROPN
ejpam-6985	20	11	functions	function	NOUN
ejpam-6985	20	12	,	,	PUNCT
ejpam-6985	20	13	co	co	NOUN
ejpam-6985	20	14	-	-	NOUN
ejpam-6985	20	15	area	area	NOUN
ejpam-6985	20	16	formulas	formula	NOUN
ejpam-6985	20	17	and	and	CCONJ
ejpam-6985	20	18	isoperimetric	isoperimetric	ADJ
ejpam-6985	20	19	control	control	NOUN
ejpam-6985	20	20	.	.	PUNCT
ejpam-6985	21	1	more	more	ADV
ejpam-6985	21	2	recently	recently	ADV
ejpam-6985	21	3	,	,	PUNCT
ejpam-6985	21	4	curvature	curvature	NOUN
ejpam-6985	21	5	-	-	PUNCT
ejpam-6985	21	6	dimension	dimension	NOUN
ejpam-6985	21	7	methods	method	NOUN
ejpam-6985	21	8	of	of	ADP
ejpam-6985	21	9	baudoin	baudoin	NOUN
ejpam-6985	21	10	and	and	CCONJ
ejpam-6985	21	11	garofalo	garofalo	NOUN
ejpam-6985	22	1	[	[	X
ejpam-6985	22	2	8	8	NUM
ejpam-6985	22	3	]	]	PUNCT
ejpam-6985	22	4	and	and	CCONJ
ejpam-6985	22	5	sharp	sharp	ADJ
ejpam-6985	22	6	inequalities	inequality	NOUN
ejpam-6985	22	7	of	of	ADP
ejpam-6985	22	8	frank	frank	PROPN
ejpam-6985	22	9	and	and	CCONJ
ejpam-6985	22	10	lieb	lieb	PROPN
ejpam-6985	22	11	[	[	X
ejpam-6985	22	12	9	9	NUM
ejpam-6985	22	13	]	]	PUNCT
ejpam-6985	22	14	have	have	AUX
ejpam-6985	22	15	advanced	advance	VERB
ejpam-6985	22	16	the	the	DET
ejpam-6985	22	17	analytic	analytic	ADJ
ejpam-6985	22	18	framework	framework	NOUN
ejpam-6985	22	19	in	in	ADP
ejpam-6985	22	20	heisenberg	heisenberg	PROPN
ejpam-6985	22	21	-	-	PUNCT
ejpam-6985	22	22	type	type	NOUN
ejpam-6985	22	23	geometries	geometry	NOUN
ejpam-6985	22	24	.	.	PUNCT
ejpam-6985	23	1	against	against	ADP
ejpam-6985	23	2	this	this	DET
ejpam-6985	23	3	background	background	NOUN
ejpam-6985	23	4	,	,	PUNCT
ejpam-6985	23	5	we	we	PRON
ejpam-6985	23	6	establish	establish	VERB
ejpam-6985	23	7	a	a	DET
ejpam-6985	23	8	cr	cr	NOUN
ejpam-6985	23	9	analogue	analogue	NOUN
ejpam-6985	23	10	of	of	ADP
ejpam-6985	23	11	cheeger	cheeger	NOUN
ejpam-6985	23	12	’s	’s	PART
ejpam-6985	23	13	inequality	inequality	NOUN
ejpam-6985	23	14	.	.	PUNCT
ejpam-6985	24	1	we	we	PRON
ejpam-6985	24	2	define	define	VERB
ejpam-6985	24	3	a	a	DET
ejpam-6985	24	4	natural	natural	ADJ
ejpam-6985	24	5	cr	cr	NOUN
ejpam-6985	24	6	cheeger	cheeger	ADV
ejpam-6985	24	7	constant	constant	VERB
ejpam-6985	24	8	hcr(m	hcr(m	ADV
ejpam-6985	24	9	)	)	PUNCT
ejpam-6985	24	10	in	in	ADP
ejpam-6985	24	11	terms	term	NOUN
ejpam-6985	24	12	of	of	ADP
ejpam-6985	24	13	horizontal	horizontal	ADJ
ejpam-6985	24	14	perimeter	perimeter	NOUN
ejpam-6985	24	15	and	and	CCONJ
ejpam-6985	24	16	contact	contact	NOUN
ejpam-6985	24	17	volume	volume	NOUN
ejpam-6985	24	18	and	and	CCONJ
ejpam-6985	24	19	prove	prove	VERB
ejpam-6985	24	20	that	that	SCONJ
ejpam-6985	24	21	the	the	DET
ejpam-6985	24	22	first	first	ADJ
ejpam-6985	24	23	positive	positive	ADJ
ejpam-6985	24	24	eigenvalue	eigenvalue	NOUN
ejpam-6985	24	25	of	of	ADP
ejpam-6985	24	26	∆b	∆b	PROPN
ejpam-6985	24	27	satisfies	satisfie	NOUN
ejpam-6985	24	28	λ1(∆b	λ1(∆b	NOUN
ejpam-6985	24	29	)	)	PUNCT
ejpam-6985	24	30	≥	≥	PROPN
ejpam-6985	24	31	c∗	c∗	PROPN
ejpam-6985	24	32	hcr(m)2	hcr(m)2	NOUN
ejpam-6985	24	33	,	,	PUNCT
ejpam-6985	24	34	where	where	SCONJ
ejpam-6985	24	35	c∗	c∗	NOUN
ejpam-6985	24	36	depends	depend	VERB
ejpam-6985	24	37	only	only	ADV
ejpam-6985	24	38	on	on	ADP
ejpam-6985	24	39	the	the	DET
ejpam-6985	24	40	homogeneous	homogeneous	ADJ
ejpam-6985	24	41	dimension	dimension	NOUN
ejpam-6985	24	42	and	and	CCONJ
ejpam-6985	24	43	on	on	ADP
ejpam-6985	24	44	controlled	control	VERB
ejpam-6985	24	45	pseudo	pseudo	NOUN
ejpam-6985	24	46	-	-	ADJ
ejpam-6985	24	47	hermitian	hermitian	ADJ
ejpam-6985	24	48	quantities	quantity	NOUN
ejpam-6985	24	49	such	such	ADJ
ejpam-6985	24	50	as	as	ADP
ejpam-6985	24	51	curvature	curvature	NOUN
ejpam-6985	24	52	and	and	CCONJ
ejpam-6985	24	53	torsion	torsion	NOUN
ejpam-6985	24	54	.	.	PUNCT
ejpam-6985	25	1	the	the	DET
ejpam-6985	25	2	proof	proof	NOUN
ejpam-6985	25	3	adapts	adapt	VERB
ejpam-6985	25	4	cheeger	cheeger	ADV
ejpam-6985	25	5	’s	’s	PART
ejpam-6985	25	6	variational	variational	ADJ
ejpam-6985	25	7	coarea	coarea	NOUN
ejpam-6985	25	8	method	method	NOUN
ejpam-6985	25	9	using	use	VERB
ejpam-6985	25	10	the	the	DET
ejpam-6985	25	11	horizontal	horizontal	ADJ
ejpam-6985	25	12	bv	bv	PROPN
ejpam-6985	25	13	framework	framework	NOUN
ejpam-6985	25	14	of	of	ADP
ejpam-6985	25	15	[	[	X
ejpam-6985	25	16	6	6	NUM
ejpam-6985	25	17	,	,	PUNCT
ejpam-6985	25	18	7	7	NUM
ejpam-6985	25	19	,	,	PUNCT
ejpam-6985	25	20	10	10	NUM
ejpam-6985	25	21	]	]	PUNCT
ejpam-6985	25	22	,	,	PUNCT
ejpam-6985	25	23	together	together	ADV
ejpam-6985	25	24	with	with	ADP
ejpam-6985	25	25	sharp	sharp	ADJ
ejpam-6985	25	26	local	local	ADJ
ejpam-6985	25	27	isoperimetric	isoperimetric	ADJ
ejpam-6985	25	28	comparisons	comparison	NOUN
ejpam-6985	25	29	.	.	PUNCT
ejpam-6985	26	1	in	in	ADP
ejpam-6985	26	2	symmetric	symmetric	ADJ
ejpam-6985	26	3	model	model	NOUN
ejpam-6985	26	4	spaces	space	NOUN
ejpam-6985	26	5	,	,	PUNCT
ejpam-6985	26	6	including	include	VERB
ejpam-6985	26	7	compact	compact	ADJ
ejpam-6985	26	8	quotients	quotient	NOUN
ejpam-6985	26	9	of	of	ADP
ejpam-6985	26	10	the	the	DET
ejpam-6985	26	11	heisenberg	heisenberg	PROPN
ejpam-6985	26	12	group	group	NOUN
ejpam-6985	26	13	and	and	CCONJ
ejpam-6985	26	14	the	the	DET
ejpam-6985	26	15	standard	standard	NOUN
ejpam-6985	26	16	cr	cr	PROPN
ejpam-6985	26	17	sphere	sphere	ADV
ejpam-6985	26	18	,	,	PUNCT
ejpam-6985	26	19	the	the	DET
ejpam-6985	26	20	optimal	optimal	ADJ
ejpam-6985	26	21	constant	constant	ADJ
ejpam-6985	26	22	c∗	c∗	NOUN
ejpam-6985	26	23	=	=	SYM
ejpam-6985	26	24	1	1	NUM
ejpam-6985	26	25	4	4	NUM
ejpam-6985	26	26	is	be	AUX
ejpam-6985	26	27	recovered	recover	VERB
ejpam-6985	26	28	,	,	PUNCT
ejpam-6985	26	29	confirming	confirm	VERB
ejpam-6985	26	30	sharpness	sharpness	NOUN
ejpam-6985	26	31	in	in	ADP
ejpam-6985	26	32	these	these	DET
ejpam-6985	26	33	cases	case	NOUN
ejpam-6985	26	34	.	.	PUNCT
ejpam-6985	27	1	in	in	ADP
ejpam-6985	27	2	addition	addition	NOUN
ejpam-6985	27	3	,	,	PUNCT
ejpam-6985	27	4	inspired	inspire	VERB
ejpam-6985	27	5	by	by	ADP
ejpam-6985	27	6	buser	buser	PROPN
ejpam-6985	27	7	’s	’s	PART
ejpam-6985	27	8	1982	1982	NUM
ejpam-6985	27	9	argument	argument	NOUN
ejpam-6985	27	10	,	,	PUNCT
ejpam-6985	27	11	we	we	PRON
ejpam-6985	27	12	establish	establish	VERB
ejpam-6985	27	13	a	a	DET
ejpam-6985	27	14	conditional	conditional	ADJ
ejpam-6985	27	15	buser	buser	NOUN
ejpam-6985	27	16	–	–	PUNCT
ejpam-6985	27	17	cr	cr	PROPN
ejpam-6985	27	18	inequality	inequality	NOUN
ejpam-6985	27	19	showing	show	VERB
ejpam-6985	27	20	that	that	SCONJ
ejpam-6985	27	21	λ1(∆b	λ1(∆b	NOUN
ejpam-6985	27	22	)	)	PUNCT
ejpam-6985	28	1	≲	≲	PROPN
ejpam-6985	28	2	hcr(m)2	hcr(m)2	VERB
ejpam-6985	28	3	+	+	CCONJ
ejpam-6985	28	4	hcr(m	hcr(m	ADV
ejpam-6985	28	5	)	)	PUNCT
ejpam-6985	28	6	,	,	PUNCT
ejpam-6985	28	7	provided	provide	VERB
ejpam-6985	28	8	the	the	DET
ejpam-6985	28	9	metric	metric	ADJ
ejpam-6985	28	10	measure	measure	NOUN
ejpam-6985	28	11	space	space	NOUN
ejpam-6985	28	12	(	(	PUNCT
ejpam-6985	28	13	m	m	PROPN
ejpam-6985	28	14	,	,	PUNCT
ejpam-6985	28	15	dcc	dcc	PROPN
ejpam-6985	28	16	,	,	PUNCT
ejpam-6985	28	17	µ	µ	NOUN
ejpam-6985	28	18	)	)	PUNCT
ejpam-6985	28	19	satisfies	satisfie	NOUN
ejpam-6985	28	20	standard	standard	ADJ
ejpam-6985	28	21	sub	sub	ADJ
ejpam-6985	28	22	-	-	ADJ
ejpam-6985	28	23	riemannian	riemannian	ADJ
ejpam-6985	28	24	analytic	analytic	ADJ
ejpam-6985	28	25	assumptions	assumption	NOUN
ejpam-6985	28	26	,	,	PUNCT
ejpam-6985	28	27	namely	namely	ADV
ejpam-6985	28	28	volume	volume	NOUN
ejpam-6985	28	29	doubling	doubling	NOUN
ejpam-6985	28	30	,	,	PUNCT
ejpam-6985	28	31	a	a	DET
ejpam-6985	28	32	(	(	PUNCT
ejpam-6985	28	33	1	1	NUM
ejpam-6985	28	34	,	,	PUNCT
ejpam-6985	28	35	1)-poincaré	1)-poincaré	NUM
ejpam-6985	28	36	inequality	inequality	NOUN
ejpam-6985	28	37	and	and	CCONJ
ejpam-6985	28	38	gaussian	gaussian	ADJ
ejpam-6985	28	39	heat	heat	NOUN
ejpam-6985	28	40	kernel	kernel	PROPN
ejpam-6985	28	41	bounds	bound	NOUN
ejpam-6985	28	42	,	,	PUNCT
ejpam-6985	28	43	as	as	ADP
ejpam-6985	28	44	in	in	ADP
ejpam-6985	28	45	the	the	DET
ejpam-6985	28	46	works	work	NOUN
ejpam-6985	28	47	of	of	ADP
ejpam-6985	28	48	jerison	jerison	PROPN
ejpam-6985	28	49	–	–	PUNCT
ejpam-6985	28	50	sánchez	sánchez	PROPN
ejpam-6985	28	51	-	-	PUNCT
ejpam-6985	28	52	calle	calle	NOUN
ejpam-6985	29	1	[	[	X
ejpam-6985	29	2	11	11	NUM
ejpam-6985	29	3	]	]	PUNCT
ejpam-6985	29	4	and	and	CCONJ
ejpam-6985	29	5	baudoin	baudoin	NUM
ejpam-6985	29	6	–	–	PUNCT
ejpam-6985	29	7	garofalo	garofalo	NOUN
ejpam-6985	29	8	[	[	X
ejpam-6985	29	9	8	8	NUM
ejpam-6985	29	10	]	]	PUNCT
ejpam-6985	29	11	.	.	PUNCT
ejpam-6985	30	1	these	these	DET
ejpam-6985	30	2	conditions	condition	NOUN
ejpam-6985	30	3	are	be	AUX
ejpam-6985	30	4	verified	verify	VERB
ejpam-6985	30	5	in	in	ADP
ejpam-6985	30	6	many	many	ADJ
ejpam-6985	30	7	natural	natural	ADJ
ejpam-6985	30	8	examples	example	NOUN
ejpam-6985	30	9	,	,	PUNCT
ejpam-6985	30	10	including	include	VERB
ejpam-6985	30	11	sasakian	sasakian	ADJ
ejpam-6985	30	12	manifolds	manifold	NOUN
ejpam-6985	30	13	and	and	CCONJ
ejpam-6985	30	14	heisenberg	heisenberg	PROPN
ejpam-6985	30	15	-	-	PUNCT
ejpam-6985	30	16	type	type	NOUN
ejpam-6985	30	17	groups	group	NOUN
ejpam-6985	30	18	and	and	CCONJ
ejpam-6985	30	19	show	show	VERB
ejpam-6985	30	20	that	that	SCONJ
ejpam-6985	30	21	the	the	DET
ejpam-6985	30	22	two	two	NUM
ejpam-6985	30	23	-	-	PUNCT
ejpam-6985	30	24	sided	sided	ADJ
ejpam-6985	30	25	spectral	spectral	ADJ
ejpam-6985	30	26	control	control	NOUN
ejpam-6985	30	27	familiar	familiar	ADJ
ejpam-6985	30	28	from	from	ADP
ejpam-6985	30	29	the	the	DET
ejpam-6985	30	30	riemannian	riemannian	ADJ
ejpam-6985	30	31	theory	theory	NOUN
ejpam-6985	30	32	extends	extend	VERB
ejpam-6985	30	33	,	,	PUNCT
ejpam-6985	30	34	in	in	ADP
ejpam-6985	30	35	an	an	DET
ejpam-6985	30	36	appropriate	appropriate	ADJ
ejpam-6985	30	37	form	form	NOUN
ejpam-6985	30	38	,	,	PUNCT
ejpam-6985	30	39	to	to	ADP
ejpam-6985	30	40	the	the	DET
ejpam-6985	30	41	cr	cr	PROPN
ejpam-6985	30	42	framework	framework	PROPN
ejpam-6985	30	43	.	.	PUNCT
ejpam-6985	31	1	finally	finally	ADV
ejpam-6985	31	2	,	,	PUNCT
ejpam-6985	31	3	to	to	PART
ejpam-6985	31	4	illustrate	illustrate	VERB
ejpam-6985	31	5	the	the	DET
ejpam-6985	31	6	scope	scope	NOUN
ejpam-6985	31	7	of	of	ADP
ejpam-6985	31	8	the	the	DET
ejpam-6985	31	9	results	result	NOUN
ejpam-6985	31	10	we	we	PRON
ejpam-6985	31	11	provide	provide	VERB
ejpam-6985	31	12	explicit	explicit	ADJ
ejpam-6985	31	13	computations	computation	NOUN
ejpam-6985	31	14	in	in	ADP
ejpam-6985	31	15	model	model	NOUN
ejpam-6985	31	16	geometries	geometry	NOUN
ejpam-6985	31	17	:	:	PUNCT
ejpam-6985	31	18	compact	compact	PROPN
ejpam-6985	31	19	heisenberg	heisenberg	PROPN
ejpam-6985	31	20	quotients	quotient	NOUN
ejpam-6985	31	21	,	,	PUNCT
ejpam-6985	31	22	the	the	DET
ejpam-6985	31	23	standard	standard	NOUN
ejpam-6985	31	24	cr	cr	PRON
ejpam-6985	31	25	sphere	sphere	ADV
ejpam-6985	31	26	s2n+1	s2n+1	PROPN
ejpam-6985	31	27	and	and	CCONJ
ejpam-6985	31	28	rossi	rossi	PROPN
ejpam-6985	31	29	’s	’s	PART
ejpam-6985	31	30	non	non	ADJ
ejpam-6985	31	31	-	-	ADJ
ejpam-6985	31	32	embeddable	embeddable	ADJ
ejpam-6985	31	33	deformations	deformation	NOUN
ejpam-6985	31	34	of	of	ADP
ejpam-6985	31	35	s3	s3	PROPN
ejpam-6985	31	36	.	.	PUNCT
ejpam-6985	32	1	these	these	DET
ejpam-6985	32	2	examples	example	NOUN
ejpam-6985	32	3	highlight	highlight	VERB
ejpam-6985	32	4	not	not	PART
ejpam-6985	32	5	only	only	ADV
ejpam-6985	32	6	the	the	DET
ejpam-6985	32	7	sharpness	sharpness	NOUN
ejpam-6985	32	8	of	of	ADP
ejpam-6985	32	9	the	the	DET
ejpam-6985	32	10	constants	constant	NOUN
ejpam-6985	32	11	but	but	CCONJ
ejpam-6985	32	12	also	also	ADV
ejpam-6985	32	13	the	the	DET
ejpam-6985	32	14	role	role	NOUN
ejpam-6985	32	15	of	of	ADP
ejpam-6985	32	16	torsion	torsion	NOUN
ejpam-6985	32	17	and	and	CCONJ
ejpam-6985	32	18	non	non	ADJ
ejpam-6985	32	19	-	-	NOUN
ejpam-6985	32	20	embeddability	embeddability	NOUN
ejpam-6985	32	21	in	in	ADP
ejpam-6985	32	22	influencing	influence	VERB
ejpam-6985	32	23	the	the	DET
ejpam-6985	32	24	spectral	spectral	ADJ
ejpam-6985	32	25	gap	gap	NOUN
ejpam-6985	32	26	.	.	PUNCT
ejpam-6985	33	1	in	in	ADP
ejpam-6985	33	2	this	this	DET
ejpam-6985	33	3	way	way	NOUN
ejpam-6985	33	4	,	,	PUNCT
ejpam-6985	33	5	the	the	DET
ejpam-6985	33	6	cr	cr	NOUN
ejpam-6985	33	7	cheeger	cheeger	PROPN
ejpam-6985	33	8	and	and	CCONJ
ejpam-6985	33	9	buser	buser	PROPN
ejpam-6985	33	10	inequalities	inequality	NOUN
ejpam-6985	33	11	we	we	PRON
ejpam-6985	33	12	establish	establish	VERB
ejpam-6985	33	13	extend	extend	VERB
ejpam-6985	33	14	a	a	DET
ejpam-6985	33	15	classical	classical	ADJ
ejpam-6985	33	16	riemannian	riemannian	ADJ
ejpam-6985	33	17	paradigm	paradigm	NOUN
ejpam-6985	33	18	into	into	ADP
ejpam-6985	33	19	the	the	DET
ejpam-6985	33	20	hypoelliptic	hypoelliptic	ADJ
ejpam-6985	33	21	setting	setting	NOUN
ejpam-6985	33	22	of	of	ADP
ejpam-6985	33	23	cr	cr	PROPN
ejpam-6985	33	24	geometry	geometry	NOUN
ejpam-6985	33	25	,	,	PUNCT
ejpam-6985	33	26	enriching	enrich	VERB
ejpam-6985	33	27	the	the	DET
ejpam-6985	33	28	broader	broad	ADJ
ejpam-6985	33	29	landscape	landscape	NOUN
ejpam-6985	33	30	of	of	ADP
ejpam-6985	33	31	cr	cr	PROPN
ejpam-6985	33	32	spectral	spectral	ADJ
ejpam-6985	33	33	theory	theory	NOUN
ejpam-6985	33	34	.	.	PUNCT
ejpam-6985	34	1	2	2	X
ejpam-6985	34	2	.	.	NUM
ejpam-6985	34	3	preliminaries	preliminary	NOUN
ejpam-6985	34	4	and	and	CCONJ
ejpam-6985	34	5	analytic	analytic	ADJ
ejpam-6985	34	6	tools	tool	NOUN
ejpam-6985	34	7	2.1	2.1	NUM
ejpam-6985	34	8	.	.	PUNCT
ejpam-6985	35	1	pseudo	pseudo	NOUN
ejpam-6985	35	2	-	-	NOUN
ejpam-6985	35	3	hermitian	hermitian	ADJ
ejpam-6985	35	4	cr	cr	PROPN
ejpam-6985	35	5	structures	structure	NOUN
ejpam-6985	35	6	let	let	VERB
ejpam-6985	35	7	m	m	PRON
ejpam-6985	35	8	be	be	AUX
ejpam-6985	35	9	a	a	DET
ejpam-6985	35	10	smooth	smooth	ADJ
ejpam-6985	35	11	,	,	PUNCT
ejpam-6985	35	12	connected	connected	ADJ
ejpam-6985	35	13	manifold	manifold	ADJ
ejpam-6985	35	14	.	.	PUNCT
ejpam-6985	36	1	a	a	DET
ejpam-6985	36	2	strictly	strictly	ADV
ejpam-6985	36	3	pseudoconvex	pseudoconvex	PROPN
ejpam-6985	36	4	pseudo	pseudo	NOUN
ejpam-6985	36	5	-	-	ADJ
ejpam-6985	36	6	hermitian	hermitian	ADJ
ejpam-6985	36	7	structure	structure	NOUN
ejpam-6985	36	8	on	on	ADP
ejpam-6985	36	9	m	m	PROPN
ejpam-6985	36	10	is	be	AUX
ejpam-6985	36	11	specified	specify	VERB
ejpam-6985	36	12	by	by	ADP
ejpam-6985	36	13	a	a	DET
ejpam-6985	36	14	contact	contact	NOUN
ejpam-6985	36	15	1	1	NUM
ejpam-6985	36	16	-	-	PUNCT
ejpam-6985	36	17	form	form	NOUN
ejpam-6985	36	18	θ	θ	NOUN
ejpam-6985	36	19	and	and	CCONJ
ejpam-6985	36	20	an	an	DET
ejpam-6985	36	21	almost	almost	ADV
ejpam-6985	36	22	complex	complex	ADJ
ejpam-6985	36	23	structure	structure	NOUN
ejpam-6985	36	24	j	j	PROPN
ejpam-6985	36	25	on	on	ADP
ejpam-6985	36	26	a.	a.	PROPN
ejpam-6985	36	27	ben	ben	PROPN
ejpam-6985	36	28	ahmed	ahmed	PROPN
ejpam-6985	36	29	/	/	SYM
ejpam-6985	36	30	eur	eur	PROPN
ejpam-6985	36	31	.	.	PUNCT
ejpam-6985	37	1	j.	j.	PROPN
ejpam-6985	37	2	pure	pure	PROPN
ejpam-6985	37	3	appl	appl	PROPN
ejpam-6985	37	4	.	.	PROPN
ejpam-6985	37	5	math	math	PROPN
ejpam-6985	37	6	,	,	PUNCT
ejpam-6985	37	7	18	18	NUM
ejpam-6985	37	8	(	(	PUNCT
ejpam-6985	37	9	4	4	NUM
ejpam-6985	37	10	)	)	PUNCT
ejpam-6985	37	11	(	(	PUNCT
ejpam-6985	37	12	2025	2025	NUM
ejpam-6985	37	13	)	)	PUNCT
ejpam-6985	37	14	,	,	PUNCT
ejpam-6985	37	15	6985	6985	NUM
ejpam-6985	37	16	3	3	NUM
ejpam-6985	37	17	of	of	ADP
ejpam-6985	37	18	16	16	NUM
ejpam-6985	37	19	the	the	DET
ejpam-6985	37	20	contact	contact	NOUN
ejpam-6985	37	21	bundle	bundle	NOUN
ejpam-6985	37	22	h	h	PROPN
ejpam-6985	38	1	=	=	PUNCT
ejpam-6985	38	2	ker	ker	NOUN
ejpam-6985	39	1	θ	θ	NOUN
ejpam-6985	39	2	such	such	ADJ
ejpam-6985	39	3	that	that	SCONJ
ejpam-6985	39	4	the	the	DET
ejpam-6985	39	5	levi	levi	PROPN
ejpam-6985	39	6	form	form	PROPN
ejpam-6985	39	7	lθ(x	lθ(x	PROPN
ejpam-6985	39	8	,	,	PUNCT
ejpam-6985	39	9	y	y	PROPN
ejpam-6985	39	10	)	)	PUNCT
ejpam-6985	39	11	:	:	PUNCT
ejpam-6985	40	1	=	=	SYM
ejpam-6985	40	2	dθ(x	dθ(x	PROPN
ejpam-6985	40	3	,	,	PUNCT
ejpam-6985	40	4	jy	jy	PROPN
ejpam-6985	40	5	)	)	PUNCT
ejpam-6985	40	6	,	,	PUNCT
ejpam-6985	40	7	x	x	X
ejpam-6985	40	8	,	,	PUNCT
ejpam-6985	40	9	y	y	PROPN
ejpam-6985	40	10	∈	∈	PROPN
ejpam-6985	40	11	γ(h	γ(h	PROPN
ejpam-6985	40	12	)	)	PUNCT
ejpam-6985	40	13	,	,	PUNCT
ejpam-6985	40	14	is	be	AUX
ejpam-6985	40	15	positive	positive	ADJ
ejpam-6985	40	16	definite	definite	ADJ
ejpam-6985	40	17	.	.	PUNCT
ejpam-6985	41	1	the	the	DET
ejpam-6985	41	2	reeb	reeb	NOUN
ejpam-6985	41	3	vector	vector	NOUN
ejpam-6985	41	4	field	field	NOUN
ejpam-6985	41	5	t	t	NOUN
ejpam-6985	41	6	satisfies	satisfie	NOUN
ejpam-6985	41	7	θ(t	θ(t	PROPN
ejpam-6985	41	8	)	)	PUNCT
ejpam-6985	42	1	=	=	SYM
ejpam-6985	42	2	1	1	NUM
ejpam-6985	42	3	,	,	PUNCT
ejpam-6985	42	4	dθ(t	dθ(t	NOUN
ejpam-6985	42	5	,	,	PUNCT
ejpam-6985	42	6	·	·	PUNCT
ejpam-6985	42	7	)	)	PUNCT
ejpam-6985	43	1	=	=	SYM
ejpam-6985	43	2	0	0	X
ejpam-6985	43	3	.	.	PUNCT
ejpam-6985	44	1	the	the	DET
ejpam-6985	44	2	natural	natural	ADJ
ejpam-6985	44	3	volume	volume	NOUN
ejpam-6985	44	4	form	form	NOUN
ejpam-6985	44	5	is	be	AUX
ejpam-6985	44	6	µ	µ	ADJ
ejpam-6985	44	7	:	:	PUNCT
ejpam-6985	44	8	=	=	SYM
ejpam-6985	44	9	θ	θ	SYM
ejpam-6985	44	10	∧	∧	PROPN
ejpam-6985	44	11	(	(	PUNCT
ejpam-6985	44	12	dθ)n	dθ)n	PROPN
ejpam-6985	44	13	,	,	PUNCT
ejpam-6985	44	14	(	(	PUNCT
ejpam-6985	44	15	2.1	2.1	NUM
ejpam-6985	44	16	)	)	PUNCT
ejpam-6985	44	17	and	and	CCONJ
ejpam-6985	44	18	the	the	DET
ejpam-6985	44	19	homogeneous	homogeneous	ADJ
ejpam-6985	44	20	dimension	dimension	NOUN
ejpam-6985	44	21	is	be	AUX
ejpam-6985	44	22	q	q	NOUN
ejpam-6985	44	23	=	=	VERB
ejpam-6985	44	24	2n+	2n+	NUM
ejpam-6985	44	25	2	2	NUM
ejpam-6985	44	26	.	.	PUNCT
ejpam-6985	45	1	given	give	VERB
ejpam-6985	45	2	a	a	DET
ejpam-6985	45	3	smooth	smooth	ADJ
ejpam-6985	45	4	function	function	NOUN
ejpam-6985	45	5	u	u	NOUN
ejpam-6985	45	6	,	,	PUNCT
ejpam-6985	45	7	its	its	PRON
ejpam-6985	45	8	horizontal	horizontal	ADJ
ejpam-6985	45	9	gradient	gradient	NOUN
ejpam-6985	45	10	∇bu	∇bu	PROPN
ejpam-6985	45	11	is	be	AUX
ejpam-6985	45	12	the	the	DET
ejpam-6985	45	13	unique	unique	ADJ
ejpam-6985	45	14	horizontal	horizontal	ADJ
ejpam-6985	45	15	vector	vector	NOUN
ejpam-6985	45	16	field	field	NOUN
ejpam-6985	45	17	satisfying	satisfy	VERB
ejpam-6985	45	18	du(x	du(x	ADV
ejpam-6985	45	19	)	)	PUNCT
ejpam-6985	46	1	=	=	SYM
ejpam-6985	46	2	lθ(∇bu	lθ(∇bu	NOUN
ejpam-6985	46	3	,	,	PUNCT
ejpam-6985	46	4	x	x	NOUN
ejpam-6985	46	5	)	)	PUNCT
ejpam-6985	46	6	for	for	ADP
ejpam-6985	46	7	all	all	DET
ejpam-6985	46	8	x	x	PROPN
ejpam-6985	46	9	∈	∈	PROPN
ejpam-6985	46	10	γ(h	γ(h	NOUN
ejpam-6985	46	11	)	)	PUNCT
ejpam-6985	46	12	.	.	PUNCT
ejpam-6985	47	1	the	the	DET
ejpam-6985	47	2	horizontal	horizontal	ADJ
ejpam-6985	47	3	divergence	divergence	NOUN
ejpam-6985	47	4	divh	divh	NOUN
ejpam-6985	47	5	computed	compute	VERB
ejpam-6985	47	6	with	with	ADP
ejpam-6985	47	7	respect	respect	NOUN
ejpam-6985	47	8	to	to	ADP
ejpam-6985	47	9	µ	µ	NOUN
ejpam-6985	47	10	yields	yield	NOUN
ejpam-6985	47	11	the	the	DET
ejpam-6985	47	12	(	(	PUNCT
ejpam-6985	47	13	positive	positive	ADJ
ejpam-6985	47	14	)	)	PUNCT
ejpam-6985	47	15	sub	sub	ADJ
ejpam-6985	47	16	-	-	ADJ
ejpam-6985	47	17	laplacian	laplacian	ADJ
ejpam-6985	47	18	∆bu	∆bu	NOUN
ejpam-6985	47	19	=	=	SYM
ejpam-6985	47	20	−	−	PROPN
ejpam-6985	47	21	divh(∇bu	divh(∇bu	NUM
ejpam-6985	47	22	)	)	PUNCT
ejpam-6985	47	23	,	,	PUNCT
ejpam-6985	47	24	(	(	PUNCT
ejpam-6985	47	25	2.2	2.2	NUM
ejpam-6985	47	26	)	)	PUNCT
ejpam-6985	47	27	which	which	PRON
ejpam-6985	47	28	is	be	AUX
ejpam-6985	47	29	essentially	essentially	ADV
ejpam-6985	47	30	self	self	NOUN
ejpam-6985	47	31	-	-	PUNCT
ejpam-6985	47	32	adjoint	adjoint	NOUN
ejpam-6985	47	33	on	on	ADP
ejpam-6985	47	34	l2(m,µ	l2(m,µ	NOUN
ejpam-6985	47	35	)	)	PUNCT
ejpam-6985	47	36	with	with	ADP
ejpam-6985	47	37	discrete	discrete	ADJ
ejpam-6985	47	38	spectrum	spectrum	NOUN
ejpam-6985	47	39	on	on	ADP
ejpam-6985	47	40	compact	compact	ADJ
ejpam-6985	47	41	m	m	PROPN
ejpam-6985	47	42	(	(	PUNCT
ejpam-6985	47	43	see	see	VERB
ejpam-6985	47	44	[	[	X
ejpam-6985	47	45	12	12	NUM
ejpam-6985	47	46	]	]	NUM
ejpam-6985	47	47	)	)	PUNCT
ejpam-6985	47	48	.	.	PUNCT
ejpam-6985	48	1	2.2	2.2	NUM
ejpam-6985	48	2	.	.	PUNCT
ejpam-6985	48	3	horizontal	horizontal	ADJ
ejpam-6985	48	4	perimeter	perimeter	NOUN
ejpam-6985	48	5	and	and	CCONJ
ejpam-6985	48	6	bv	bv	PROPN
ejpam-6985	48	7	functions	function	VERB
ejpam-6985	48	8	a	a	DET
ejpam-6985	48	9	key	key	ADJ
ejpam-6985	48	10	analytic	analytic	ADJ
ejpam-6985	48	11	tool	tool	NOUN
ejpam-6985	48	12	in	in	ADP
ejpam-6985	48	13	extending	extend	VERB
ejpam-6985	48	14	isoperimetric	isoperimetric	ADJ
ejpam-6985	48	15	methods	method	NOUN
ejpam-6985	48	16	to	to	ADP
ejpam-6985	48	17	the	the	DET
ejpam-6985	48	18	cr	cr	NOUN
ejpam-6985	48	19	setting	set	VERB
ejpam-6985	48	20	is	be	AUX
ejpam-6985	48	21	the	the	DET
ejpam-6985	48	22	notion	notion	NOUN
ejpam-6985	48	23	of	of	ADP
ejpam-6985	48	24	perimeter	perimeter	NOUN
ejpam-6985	48	25	adapted	adapt	VERB
ejpam-6985	48	26	to	to	ADP
ejpam-6985	48	27	the	the	DET
ejpam-6985	48	28	horizontal	horizontal	ADJ
ejpam-6985	48	29	distribution	distribution	NOUN
ejpam-6985	48	30	.	.	PUNCT
ejpam-6985	49	1	this	this	PRON
ejpam-6985	49	2	is	be	AUX
ejpam-6985	49	3	provided	provide	VERB
ejpam-6985	49	4	by	by	ADP
ejpam-6985	49	5	horizontal	horizontal	ADJ
ejpam-6985	49	6	bounded	bounded	ADJ
ejpam-6985	49	7	variation	variation	NOUN
ejpam-6985	49	8	(	(	PUNCT
ejpam-6985	49	9	bvh	bvh	NOUN
ejpam-6985	49	10	)	)	PUNCT
ejpam-6985	49	11	theory	theory	NOUN
ejpam-6985	49	12	,	,	PUNCT
ejpam-6985	49	13	developed	develop	VERB
ejpam-6985	49	14	by	by	ADP
ejpam-6985	49	15	franchi	franchi	PROPN
ejpam-6985	49	16	–	–	PUNCT
ejpam-6985	49	17	serapioni	serapioni	NOUN
ejpam-6985	49	18	–	–	PUNCT
ejpam-6985	49	19	serra	serra	PROPN
ejpam-6985	49	20	cassano	cassano	PROPN
ejpam-6985	50	1	[	[	X
ejpam-6985	50	2	6	6	NUM
ejpam-6985	50	3	]	]	PUNCT
ejpam-6985	50	4	and	and	CCONJ
ejpam-6985	50	5	further	far	ADV
ejpam-6985	50	6	refined	refine	VERB
ejpam-6985	50	7	in	in	ADP
ejpam-6985	50	8	[	[	X
ejpam-6985	50	9	7	7	NUM
ejpam-6985	50	10	]	]	PUNCT
ejpam-6985	50	11	.	.	PUNCT
ejpam-6985	51	1	in	in	ADP
ejpam-6985	51	2	this	this	DET
ejpam-6985	51	3	subsection	subsection	NOUN
ejpam-6985	51	4	we	we	PRON
ejpam-6985	51	5	recall	recall	VERB
ejpam-6985	51	6	the	the	DET
ejpam-6985	51	7	necessary	necessary	ADJ
ejpam-6985	51	8	framework	framework	NOUN
ejpam-6985	51	9	.	.	PUNCT
ejpam-6985	52	1	horizontal	horizontal	ADJ
ejpam-6985	52	2	variation	variation	NOUN
ejpam-6985	52	3	.	.	PUNCT
ejpam-6985	53	1	let	let	VERB
ejpam-6985	53	2	u	u	PRON
ejpam-6985	53	3	∈	∈	PROPN
ejpam-6985	53	4	l1(m	l1(m	PROPN
ejpam-6985	53	5	)	)	PUNCT
ejpam-6985	53	6	,	,	PUNCT
ejpam-6985	53	7	where	where	SCONJ
ejpam-6985	53	8	m	m	NOUN
ejpam-6985	53	9	is	be	AUX
ejpam-6985	53	10	a	a	DET
ejpam-6985	53	11	compact	compact	ADJ
ejpam-6985	53	12	strictly	strictly	ADV
ejpam-6985	53	13	pseudoconvex	pseudoconvex	VERB
ejpam-6985	53	14	pseudo	pseudo	NOUN
ejpam-6985	53	15	-	-	ADJ
ejpam-6985	53	16	hermitian	hermitian	ADJ
ejpam-6985	53	17	cr	cr	PROPN
ejpam-6985	53	18	manifold	manifold	ADJ
ejpam-6985	53	19	with	with	ADP
ejpam-6985	53	20	contact	contact	NOUN
ejpam-6985	53	21	volume	volume	NOUN
ejpam-6985	53	22	µ	µ	X
ejpam-6985	53	23	=	=	SYM
ejpam-6985	53	24	θ	θ	X
ejpam-6985	53	25	∧	∧	PROPN
ejpam-6985	53	26	(	(	PUNCT
ejpam-6985	53	27	dθ)n	dθ)n	PROPN
ejpam-6985	53	28	.	.	PUNCT
ejpam-6985	54	1	the	the	DET
ejpam-6985	54	2	horizontal	horizontal	ADJ
ejpam-6985	54	3	total	total	ADJ
ejpam-6985	54	4	variation	variation	NOUN
ejpam-6985	54	5	of	of	ADP
ejpam-6985	54	6	u	u	NOUN
ejpam-6985	54	7	is	be	AUX
ejpam-6985	54	8	defined	define	VERB
ejpam-6985	54	9	by	by	ADP
ejpam-6985	54	10	|du|h(m	|du|h(m	NOUN
ejpam-6985	54	11	)	)	PUNCT
ejpam-6985	54	12	=	=	SYM
ejpam-6985	54	13	sup	sup	X
ejpam-6985	54	14	{	{	PUNCT
ejpam-6985	54	15	∫	∫	PROPN
ejpam-6985	54	16	m	m	PROPN
ejpam-6985	54	17	u	u	NOUN
ejpam-6985	54	18	divµ	divµ	PROPN
ejpam-6985	54	19	φ	φ	PROPN
ejpam-6985	54	20	dµ	dµ	PROPN
ejpam-6985	54	21	:	:	PUNCT
ejpam-6985	54	22	φ	φ	PROPN
ejpam-6985	54	23	∈	∈	PROPN
ejpam-6985	54	24	c1	c1	PROPN
ejpam-6985	54	25	c	c	PROPN
ejpam-6985	54	26	(	(	PUNCT
ejpam-6985	54	27	m	m	PROPN
ejpam-6985	54	28	;	;	PUNCT
ejpam-6985	54	29	h	h	X
ejpam-6985	54	30	)	)	PUNCT
ejpam-6985	54	31	,	,	PUNCT
ejpam-6985	54	32	∥φ∥∞	∥φ∥∞	NUM
ejpam-6985	54	33	≤	≤	NUM
ejpam-6985	54	34	1	1	NUM
ejpam-6985	54	35	}	}	PUNCT
ejpam-6985	54	36	,	,	PUNCT
ejpam-6985	54	37	(	(	PUNCT
ejpam-6985	54	38	2.3	2.3	NUM
ejpam-6985	54	39	)	)	PUNCT
ejpam-6985	54	40	where	where	SCONJ
ejpam-6985	54	41	divµ	divµ	NOUN
ejpam-6985	54	42	is	be	AUX
ejpam-6985	54	43	the	the	DET
ejpam-6985	54	44	horizontal	horizontal	ADJ
ejpam-6985	54	45	divergence	divergence	NOUN
ejpam-6985	54	46	with	with	ADP
ejpam-6985	54	47	respect	respect	NOUN
ejpam-6985	54	48	to	to	ADP
ejpam-6985	54	49	µ.	µ.	NOUN
ejpam-6985	54	50	we	we	PRON
ejpam-6985	54	51	say	say	VERB
ejpam-6985	54	52	u	u	PROPN
ejpam-6985	54	53	∈	∈	PROPN
ejpam-6985	54	54	bvh(m	bvh(m	PROPN
ejpam-6985	54	55	)	)	PUNCT
ejpam-6985	54	56	if	if	SCONJ
ejpam-6985	54	57	|du|h(m	|du|h(m	NOUN
ejpam-6985	54	58	)	)	PUNCT
ejpam-6985	55	1	<	<	X
ejpam-6985	55	2	∞.	∞.	PROPN
ejpam-6985	55	3	horizontal	horizontal	ADJ
ejpam-6985	55	4	perimeter	perimeter	NOUN
ejpam-6985	55	5	.	.	PUNCT
ejpam-6985	56	1	for	for	ADP
ejpam-6985	56	2	a	a	DET
ejpam-6985	56	3	measurable	measurable	ADJ
ejpam-6985	56	4	set	set	NOUN
ejpam-6985	56	5	e	e	SYM
ejpam-6985	56	6	⊂m	⊂m	PROPN
ejpam-6985	56	7	with	with	ADP
ejpam-6985	56	8	finite	finite	ADJ
ejpam-6985	56	9	horizontal	horizontal	ADJ
ejpam-6985	56	10	variation	variation	NOUN
ejpam-6985	56	11	of	of	ADP
ejpam-6985	56	12	its	its	PRON
ejpam-6985	56	13	indicator	indicator	NOUN
ejpam-6985	56	14	function	function	NOUN
ejpam-6985	56	15	,	,	PUNCT
ejpam-6985	56	16	the	the	DET
ejpam-6985	56	17	horizontal	horizontal	ADJ
ejpam-6985	56	18	perimeter	perimeter	NOUN
ejpam-6985	56	19	of	of	ADP
ejpam-6985	56	20	e	e	PROPN
ejpam-6985	56	21	in	in	ADP
ejpam-6985	56	22	m	m	PROPN
ejpam-6985	56	23	is	be	AUX
ejpam-6985	56	24	defined	define	VERB
ejpam-6985	56	25	by	by	ADP
ejpam-6985	56	26	perh(e;m	perh(e;m	NOUN
ejpam-6985	56	27	)	)	PUNCT
ejpam-6985	56	28	:	:	PUNCT
ejpam-6985	57	1	=	=	PUNCT
ejpam-6985	57	2	|d1e	|d1e	NOUN
ejpam-6985	57	3	|h(m	|h(m	NOUN
ejpam-6985	57	4	)	)	PUNCT
ejpam-6985	57	5	.	.	PUNCT
ejpam-6985	58	1	this	this	PRON
ejpam-6985	58	2	generalizes	generalize	VERB
ejpam-6985	58	3	the	the	DET
ejpam-6985	58	4	riemannian	riemannian	ADJ
ejpam-6985	58	5	notion	notion	NOUN
ejpam-6985	58	6	of	of	ADP
ejpam-6985	58	7	perimeter	perimeter	NOUN
ejpam-6985	58	8	to	to	ADP
ejpam-6985	58	9	the	the	DET
ejpam-6985	58	10	cr	cr	PROPN
ejpam-6985	58	11	framework	framework	PROPN
ejpam-6985	58	12	.	.	PUNCT
ejpam-6985	59	1	proposition	proposition	NOUN
ejpam-6985	59	2	1	1	NUM
ejpam-6985	59	3	(	(	PUNCT
ejpam-6985	59	4	horizontal	horizontal	ADJ
ejpam-6985	59	5	co	co	NOUN
ejpam-6985	59	6	-	-	NOUN
ejpam-6985	59	7	area	area	NOUN
ejpam-6985	59	8	formula	formula	NOUN
ejpam-6985	59	9	;	;	PUNCT
ejpam-6985	59	10	[	[	X
ejpam-6985	59	11	6	6	NUM
ejpam-6985	59	12	,	,	PUNCT
ejpam-6985	59	13	7	7	NUM
ejpam-6985	59	14	]	]	NUM
ejpam-6985	59	15	)	)	PUNCT
ejpam-6985	59	16	.	.	PUNCT
ejpam-6985	60	1	if	if	SCONJ
ejpam-6985	60	2	u	u	PROPN
ejpam-6985	60	3	∈	∈	PROPN
ejpam-6985	60	4	bvh(m	bvh(m	PROPN
ejpam-6985	60	5	)	)	PUNCT
ejpam-6985	60	6	,	,	PUNCT
ejpam-6985	60	7	then	then	ADV
ejpam-6985	60	8	|du|h(m	|du|h(m	VERB
ejpam-6985	60	9	)	)	PUNCT
ejpam-6985	60	10	=	=	SYM
ejpam-6985	61	1	∫	∫	PROPN
ejpam-6985	62	1	+	+	NUM
ejpam-6985	62	2	∞	∞	PROPN
ejpam-6985	62	3	−∞	−∞	ADP
ejpam-6985	62	4	perh({u	perh({u	PROPN
ejpam-6985	62	5	>	>	PUNCT
ejpam-6985	62	6	t};m	t};m	PROPN
ejpam-6985	62	7	)	)	PUNCT
ejpam-6985	62	8	dt	dt	NOUN
ejpam-6985	62	9	.	.	PUNCT
ejpam-6985	63	1	(	(	PUNCT
ejpam-6985	63	2	2.4	2.4	NUM
ejpam-6985	63	3	)	)	PUNCT
ejpam-6985	63	4	moreover	moreover	ADV
ejpam-6985	63	5	,	,	PUNCT
ejpam-6985	63	6	if	if	SCONJ
ejpam-6985	63	7	u	u	PROPN
ejpam-6985	63	8	∈	∈	PROPN
ejpam-6985	63	9	lip(m	lip(m	PROPN
ejpam-6985	63	10	)	)	PUNCT
ejpam-6985	63	11	,	,	PUNCT
ejpam-6985	63	12	then	then	ADV
ejpam-6985	63	13	|du|h(m	|du|h(m	VERB
ejpam-6985	63	14	)	)	PUNCT
ejpam-6985	64	1	=	=	SYM
ejpam-6985	65	1	∫	∫	PROPN
ejpam-6985	65	2	m	m	PROPN
ejpam-6985	65	3	|∇bu|	|∇bu|	PROPN
ejpam-6985	65	4	dµ.	dµ.	PROPN
ejpam-6985	65	5	(	(	PUNCT
ejpam-6985	65	6	2.5	2.5	NUM
ejpam-6985	65	7	)	)	PUNCT
ejpam-6985	65	8	a.	a.	NOUN
ejpam-6985	65	9	ben	ben	PROPN
ejpam-6985	65	10	ahmed	ahmed	PROPN
ejpam-6985	65	11	/	/	SYM
ejpam-6985	65	12	eur	eur	PROPN
ejpam-6985	65	13	.	.	PUNCT
ejpam-6985	66	1	j.	j.	PROPN
ejpam-6985	66	2	pure	pure	PROPN
ejpam-6985	66	3	appl	appl	PROPN
ejpam-6985	66	4	.	.	PROPN
ejpam-6985	66	5	math	math	PROPN
ejpam-6985	66	6	,	,	PUNCT
ejpam-6985	66	7	18	18	NUM
ejpam-6985	66	8	(	(	PUNCT
ejpam-6985	66	9	4	4	NUM
ejpam-6985	66	10	)	)	PUNCT
ejpam-6985	66	11	(	(	PUNCT
ejpam-6985	66	12	2025	2025	NUM
ejpam-6985	66	13	)	)	PUNCT
ejpam-6985	66	14	,	,	PUNCT
ejpam-6985	66	15	6985	6985	NUM
ejpam-6985	66	16	4	4	NUM
ejpam-6985	66	17	of	of	ADP
ejpam-6985	66	18	16	16	NUM
ejpam-6985	66	19	proof	proof	NOUN
ejpam-6985	66	20	.	.	PUNCT
ejpam-6985	67	1	we	we	PRON
ejpam-6985	67	2	present	present	VERB
ejpam-6985	67	3	a	a	DET
ejpam-6985	67	4	systematic	systematic	ADJ
ejpam-6985	67	5	argument	argument	NOUN
ejpam-6985	67	6	in	in	ADP
ejpam-6985	67	7	three	three	NUM
ejpam-6985	67	8	steps	step	NOUN
ejpam-6985	67	9	.	.	PUNCT
ejpam-6985	68	1	step	step	NOUN
ejpam-6985	68	2	1	1	NUM
ejpam-6985	68	3	:	:	PUNCT
ejpam-6985	68	4	the	the	DET
ejpam-6985	68	5	smooth	smooth	ADJ
ejpam-6985	68	6	case	case	NOUN
ejpam-6985	68	7	.	.	PUNCT
ejpam-6985	69	1	suppose	suppose	VERB
ejpam-6985	69	2	u	u	PRON
ejpam-6985	69	3	∈	∈	PROPN
ejpam-6985	69	4	c∞(m	c∞(m	NOUN
ejpam-6985	69	5	)	)	PUNCT
ejpam-6985	69	6	.	.	PUNCT
ejpam-6985	70	1	for	for	ADP
ejpam-6985	70	2	a	a	DET
ejpam-6985	70	3	regular	regular	ADJ
ejpam-6985	70	4	value	value	NOUN
ejpam-6985	70	5	t	t	NOUN
ejpam-6985	70	6	,	,	PUNCT
ejpam-6985	70	7	let	let	VERB
ejpam-6985	70	8	et	et	NOUN
ejpam-6985	70	9	=	=	PRON
ejpam-6985	70	10	{	{	PUNCT
ejpam-6985	70	11	u	u	X
ejpam-6985	70	12	>	>	X
ejpam-6985	70	13	t	t	PROPN
ejpam-6985	70	14	}	}	PUNCT
ejpam-6985	70	15	.	.	PUNCT
ejpam-6985	71	1	the	the	DET
ejpam-6985	71	2	level	level	NOUN
ejpam-6985	71	3	set	set	NOUN
ejpam-6985	71	4	{	{	PUNCT
ejpam-6985	71	5	u	u	NOUN
ejpam-6985	71	6	=	=	PROPN
ejpam-6985	71	7	t	t	PROPN
ejpam-6985	71	8	}	}	PUNCT
ejpam-6985	71	9	is	be	AUX
ejpam-6985	71	10	a	a	DET
ejpam-6985	71	11	smooth	smooth	ADJ
ejpam-6985	71	12	hypersurface	hypersurface	NOUN
ejpam-6985	71	13	with	with	ADP
ejpam-6985	71	14	riemannian	riemannian	ADJ
ejpam-6985	71	15	unit	unit	NOUN
ejpam-6985	71	16	normal	normal	ADJ
ejpam-6985	71	17	n	n	PROPN
ejpam-6985	71	18	=	=	SYM
ejpam-6985	71	19	∇u/|∇u|	∇u/|∇u|	PROPN
ejpam-6985	71	20	.	.	PUNCT
ejpam-6985	72	1	writing	write	VERB
ejpam-6985	72	2	nh	nh	PROPN
ejpam-6985	72	3	for	for	ADP
ejpam-6985	72	4	the	the	DET
ejpam-6985	72	5	projection	projection	NOUN
ejpam-6985	72	6	of	of	ADP
ejpam-6985	72	7	n	n	NOUN
ejpam-6985	72	8	onto	onto	ADP
ejpam-6985	72	9	the	the	DET
ejpam-6985	72	10	horizontal	horizontal	ADJ
ejpam-6985	72	11	bundle	bundle	PROPN
ejpam-6985	72	12	h	h	PROPN
ejpam-6985	72	13	,	,	PUNCT
ejpam-6985	72	14	one	one	NUM
ejpam-6985	72	15	has	have	VERB
ejpam-6985	72	16	|nh	|nh	NUM
ejpam-6985	72	17	|	|	NOUN
ejpam-6985	72	18	=	=	SYM
ejpam-6985	72	19	|∇bu|/|∇u|	|∇bu|/|∇u|	PROPN
ejpam-6985	72	20	.	.	PUNCT
ejpam-6985	73	1	by	by	ADP
ejpam-6985	73	2	the	the	DET
ejpam-6985	73	3	characterization	characterization	NOUN
ejpam-6985	73	4	of	of	ADP
ejpam-6985	73	5	horizontal	horizontal	ADJ
ejpam-6985	73	6	perimeter	perimeter	NOUN
ejpam-6985	73	7	for	for	ADP
ejpam-6985	73	8	smooth	smooth	ADJ
ejpam-6985	73	9	sets	set	NOUN
ejpam-6985	73	10	[	[	X
ejpam-6985	73	11	6	6	NUM
ejpam-6985	73	12	]	]	PUNCT
ejpam-6985	73	13	,	,	PUNCT
ejpam-6985	73	14	perh(et;m	perh(et;m	X
ejpam-6985	73	15	)	)	PUNCT
ejpam-6985	73	16	=	=	SYM
ejpam-6985	73	17	∫	∫	PROPN
ejpam-6985	73	18	{	{	PUNCT
ejpam-6985	73	19	u	u	PROPN
ejpam-6985	73	20	=	=	PROPN
ejpam-6985	73	21	t	t	X
ejpam-6985	73	22	}	}	PUNCT
ejpam-6985	73	23	|nh	|nh	NUM
ejpam-6985	73	24	|	|	ADV
ejpam-6985	73	25	dσt	dσt	NOUN
ejpam-6985	73	26	=	=	SYM
ejpam-6985	73	27	∫	∫	PROPN
ejpam-6985	73	28	{	{	PUNCT
ejpam-6985	73	29	u	u	PROPN
ejpam-6985	73	30	=	=	PROPN
ejpam-6985	73	31	t	t	PROPN
ejpam-6985	73	32	}	}	PUNCT
ejpam-6985	73	33	|∇bu|	|∇bu|	NOUN
ejpam-6985	73	34	|∇u|	|∇u|	PROPN
ejpam-6985	73	35	dσt	dσt	PROPN
ejpam-6985	73	36	,	,	PUNCT
ejpam-6985	73	37	where	where	SCONJ
ejpam-6985	73	38	dσt	dσt	NOUN
ejpam-6985	73	39	is	be	AUX
ejpam-6985	73	40	the	the	DET
ejpam-6985	73	41	induced	induced	ADJ
ejpam-6985	73	42	surface	surface	NOUN
ejpam-6985	73	43	measure	measure	NOUN
ejpam-6985	73	44	.	.	PUNCT
ejpam-6985	74	1	applying	apply	VERB
ejpam-6985	74	2	the	the	DET
ejpam-6985	74	3	classical	classical	ADJ
ejpam-6985	74	4	riemannian	riemannian	ADJ
ejpam-6985	74	5	co	co	NOUN
ejpam-6985	74	6	-	-	NOUN
ejpam-6985	74	7	area	area	NOUN
ejpam-6985	74	8	formula	formula	NOUN
ejpam-6985	74	9	to	to	ADP
ejpam-6985	74	10	the	the	DET
ejpam-6985	74	11	integrand	integrand	PROPN
ejpam-6985	74	12	ψ(x	ψ(x	NOUN
ejpam-6985	74	13	)	)	PUNCT
ejpam-6985	75	1	=	=	SYM
ejpam-6985	75	2	|∇bu(x)|/|∇u(x)|	|∇bu(x)|/|∇u(x)|	VERB
ejpam-6985	75	3	yields∫	yields∫	NOUN
ejpam-6985	75	4	m	m	VERB
ejpam-6985	75	5	|∇bu|	|∇bu|	NOUN
ejpam-6985	75	6	dµ	dµ	PROPN
ejpam-6985	75	7	=	=	SYM
ejpam-6985	75	8	∫	∫	PROPN
ejpam-6985	76	1	+	+	NUM
ejpam-6985	76	2	∞	∞	PROPN
ejpam-6985	76	3	−∞	−∞	ADP
ejpam-6985	76	4	perh(et;m	perh(et;m	NOUN
ejpam-6985	76	5	)	)	PUNCT
ejpam-6985	76	6	dt	dt	PROPN
ejpam-6985	76	7	.	.	PUNCT
ejpam-6985	77	1	this	this	PRON
ejpam-6985	77	2	proves	prove	VERB
ejpam-6985	77	3	both	both	DET
ejpam-6985	77	4	(	(	PUNCT
ejpam-6985	77	5	2.4	2.4	NUM
ejpam-6985	77	6	)	)	PUNCT
ejpam-6985	77	7	and	and	CCONJ
ejpam-6985	77	8	(	(	PUNCT
ejpam-6985	77	9	2.5	2.5	NUM
ejpam-6985	77	10	)	)	PUNCT
ejpam-6985	77	11	for	for	ADP
ejpam-6985	77	12	smooth	smooth	ADJ
ejpam-6985	77	13	u.	u.	NOUN
ejpam-6985	77	14	step	step	NOUN
ejpam-6985	77	15	2	2	NUM
ejpam-6985	77	16	:	:	PUNCT
ejpam-6985	77	17	extension	extension	NOUN
ejpam-6985	77	18	to	to	ADP
ejpam-6985	77	19	bvh	bvh	NOUN
ejpam-6985	77	20	.	.	PUNCT
ejpam-6985	78	1	let	let	VERB
ejpam-6985	78	2	u	u	PRON
ejpam-6985	78	3	∈	∈	PROPN
ejpam-6985	78	4	bvh(m	bvh(m	PROPN
ejpam-6985	78	5	)	)	PUNCT
ejpam-6985	78	6	.	.	PUNCT
ejpam-6985	79	1	by	by	ADP
ejpam-6985	79	2	the	the	DET
ejpam-6985	79	3	approximation	approximation	NOUN
ejpam-6985	79	4	theorem	theorem	NOUN
ejpam-6985	79	5	in	in	ADP
ejpam-6985	79	6	horizontal	horizontal	PROPN
ejpam-6985	79	7	bv	bv	PROPN
ejpam-6985	79	8	theory	theory	NOUN
ejpam-6985	79	9	[	[	X
ejpam-6985	79	10	6	6	NUM
ejpam-6985	79	11	,	,	PUNCT
ejpam-6985	79	12	thm	thm	PROPN
ejpam-6985	79	13	.	.	PUNCT
ejpam-6985	79	14	3.1	3.1	NUM
ejpam-6985	79	15	]	]	PUNCT
ejpam-6985	79	16	,	,	PUNCT
ejpam-6985	79	17	there	there	PRON
ejpam-6985	79	18	exists	exist	VERB
ejpam-6985	79	19	a	a	DET
ejpam-6985	79	20	sequence	sequence	NOUN
ejpam-6985	79	21	uk	uk	PROPN
ejpam-6985	79	22	∈	∈	PROPN
ejpam-6985	79	23	c∞(m	c∞(m	NOUN
ejpam-6985	79	24	)	)	PUNCT
ejpam-6985	79	25	such	such	ADJ
ejpam-6985	79	26	that	that	SCONJ
ejpam-6985	79	27	uk	uk	PROPN
ejpam-6985	79	28	→	→	SYM
ejpam-6985	79	29	u	u	PROPN
ejpam-6985	79	30	in	in	ADP
ejpam-6985	79	31	l1(m	l1(m	PROPN
ejpam-6985	79	32	)	)	PUNCT
ejpam-6985	79	33	and	and	CCONJ
ejpam-6985	79	34	|duk|h(m	|duk|h(m	NOUN
ejpam-6985	79	35	)	)	PUNCT
ejpam-6985	79	36	→	→	SYM
ejpam-6985	79	37	|du|h(m	|du|h(m	NOUN
ejpam-6985	79	38	)	)	PUNCT
ejpam-6985	79	39	.	.	PUNCT
ejpam-6985	80	1	from	from	ADP
ejpam-6985	80	2	step	step	NOUN
ejpam-6985	80	3	1	1	NUM
ejpam-6985	80	4	,	,	PUNCT
ejpam-6985	80	5	|duk|h(m	|duk|h(m	NOUN
ejpam-6985	80	6	)	)	PUNCT
ejpam-6985	80	7	=	=	SYM
ejpam-6985	81	1	∫	∫	PROPN
ejpam-6985	82	1	+	+	NUM
ejpam-6985	82	2	∞	∞	PROPN
ejpam-6985	82	3	−∞	−∞	ADP
ejpam-6985	82	4	perh({uk	perh({uk	PROPN
ejpam-6985	82	5	>	>	X
ejpam-6985	82	6	t};m	t};m	NOUN
ejpam-6985	82	7	)	)	PUNCT
ejpam-6985	82	8	dt	dt	NOUN
ejpam-6985	82	9	.	.	PUNCT
ejpam-6985	83	1	by	by	ADP
ejpam-6985	83	2	convergence	convergence	NOUN
ejpam-6985	83	3	in	in	ADP
ejpam-6985	83	4	measure	measure	NOUN
ejpam-6985	83	5	,	,	PUNCT
ejpam-6985	83	6	1{uk	1{uk	NOUN
ejpam-6985	83	7	>	>	X
ejpam-6985	83	8	t	t	PROPN
ejpam-6985	83	9	}	}	PUNCT
ejpam-6985	83	10	→	→	SYM
ejpam-6985	83	11	1{u	1{u	NUM
ejpam-6985	83	12	>	>	SYM
ejpam-6985	83	13	t	t	NOUN
ejpam-6985	83	14	}	}	PUNCT
ejpam-6985	83	15	for	for	ADP
ejpam-6985	83	16	a.e	a.e	PROPN
ejpam-6985	83	17	.	.	PROPN
ejpam-6985	83	18	t	t	PROPN
ejpam-6985	83	19	and	and	CCONJ
ejpam-6985	83	20	by	by	ADP
ejpam-6985	83	21	lower	low	ADJ
ejpam-6985	83	22	semicontinuity	semicontinuity	NOUN
ejpam-6985	83	23	of	of	ADP
ejpam-6985	83	24	perimeter	perimeter	NOUN
ejpam-6985	83	25	[	[	X
ejpam-6985	83	26	6	6	NUM
ejpam-6985	83	27	,	,	PUNCT
ejpam-6985	83	28	thm	thm	PROPN
ejpam-6985	83	29	.	.	PUNCT
ejpam-6985	83	30	4.2	4.2	NUM
ejpam-6985	83	31	]	]	PUNCT
ejpam-6985	83	32	,	,	PUNCT
ejpam-6985	83	33	perh({u	perh({u	PROPN
ejpam-6985	83	34	>	>	SYM
ejpam-6985	83	35	t};m	t};m	NOUN
ejpam-6985	83	36	)	)	PUNCT
ejpam-6985	83	37	≤	≤	PROPN
ejpam-6985	83	38	lim	lim	PROPN
ejpam-6985	83	39	inf	inf	PROPN
ejpam-6985	83	40	k→∞	k→∞	PROPN
ejpam-6985	83	41	perh({uk	perh({uk	PROPN
ejpam-6985	83	42	>	>	X
ejpam-6985	83	43	t};m	t};m	NOUN
ejpam-6985	83	44	)	)	PUNCT
ejpam-6985	83	45	.	.	PUNCT
ejpam-6985	84	1	integrating	integrate	VERB
ejpam-6985	84	2	and	and	CCONJ
ejpam-6985	84	3	applying	apply	VERB
ejpam-6985	84	4	fatou	fatou	NOUN
ejpam-6985	84	5	’s	’s	PART
ejpam-6985	84	6	lemma	lemma	PROPN
ejpam-6985	84	7	gives∫	gives∫	PROPN
ejpam-6985	84	8	+	+	PROPN
ejpam-6985	84	9	∞	∞	PROPN
ejpam-6985	84	10	−∞	−∞	ADP
ejpam-6985	84	11	perh({u	perh({u	PROPN
ejpam-6985	84	12	>	>	PUNCT
ejpam-6985	84	13	t};m	t};m	NOUN
ejpam-6985	84	14	)	)	PUNCT
ejpam-6985	84	15	dt	dt	PART
ejpam-6985	85	1	≤	≤	NUM
ejpam-6985	85	2	|du|h(m	|du|h(m	NOUN
ejpam-6985	85	3	)	)	PUNCT
ejpam-6985	85	4	.	.	PUNCT
ejpam-6985	86	1	the	the	DET
ejpam-6985	86	2	reverse	reverse	ADJ
ejpam-6985	86	3	inequality	inequality	NOUN
ejpam-6985	86	4	follows	follow	VERB
ejpam-6985	86	5	by	by	ADP
ejpam-6985	86	6	the	the	DET
ejpam-6985	86	7	layer	layer	NOUN
ejpam-6985	86	8	-	-	PUNCT
ejpam-6985	86	9	cake	cake	NOUN
ejpam-6985	86	10	representation	representation	NOUN
ejpam-6985	86	11	of	of	ADP
ejpam-6985	86	12	u	u	PRON
ejpam-6985	86	13	combined	combine	VERB
ejpam-6985	86	14	with	with	ADP
ejpam-6985	86	15	the	the	DET
ejpam-6985	86	16	definition	definition	NOUN
ejpam-6985	86	17	of	of	ADP
ejpam-6985	86	18	perimeter	perimeter	NOUN
ejpam-6985	86	19	(	(	PUNCT
ejpam-6985	86	20	see	see	VERB
ejpam-6985	86	21	[	[	X
ejpam-6985	86	22	7	7	NUM
ejpam-6985	86	23	]	]	NUM
ejpam-6985	86	24	)	)	PUNCT
ejpam-6985	86	25	.	.	PUNCT
ejpam-6985	87	1	thus	thus	ADV
ejpam-6985	87	2	equality	equality	NOUN
ejpam-6985	87	3	holds	hold	VERB
ejpam-6985	87	4	,	,	PUNCT
ejpam-6985	87	5	proving	prove	VERB
ejpam-6985	87	6	(	(	PUNCT
ejpam-6985	87	7	2.4	2.4	NUM
ejpam-6985	87	8	)	)	PUNCT
ejpam-6985	87	9	.	.	PUNCT
ejpam-6985	88	1	step	step	NOUN
ejpam-6985	88	2	3	3	NUM
ejpam-6985	88	3	:	:	PUNCT
ejpam-6985	88	4	lipschitz	lipschitz	NOUN
ejpam-6985	88	5	functions	function	NOUN
ejpam-6985	88	6	.	.	PUNCT
ejpam-6985	89	1	if	if	SCONJ
ejpam-6985	89	2	u	u	PROPN
ejpam-6985	89	3	∈	∈	PROPN
ejpam-6985	89	4	lip(m	lip(m	PROPN
ejpam-6985	89	5	)	)	PUNCT
ejpam-6985	89	6	,	,	PUNCT
ejpam-6985	89	7	then	then	ADV
ejpam-6985	89	8	∇bu	∇bu	PROPN
ejpam-6985	89	9	exists	exist	VERB
ejpam-6985	89	10	µ-a.e	µ-a.e	NOUN
ejpam-6985	89	11	.	.	PUNCT
ejpam-6985	90	1	by	by	ADP
ejpam-6985	90	2	rademacher	rademacher	PROPN
ejpam-6985	90	3	’s	’s	PART
ejpam-6985	90	4	theorem	theorem	NOUN
ejpam-6985	90	5	in	in	ADP
ejpam-6985	90	6	carnot	carnot	NOUN
ejpam-6985	90	7	–	–	PUNCT
ejpam-6985	90	8	carathéodory	carathéodory	NOUN
ejpam-6985	90	9	spaces	space	NOUN
ejpam-6985	90	10	[	[	X
ejpam-6985	90	11	7	7	NUM
ejpam-6985	90	12	]	]	PUNCT
ejpam-6985	90	13	.	.	PUNCT
ejpam-6985	91	1	using	use	VERB
ejpam-6985	91	2	(	(	PUNCT
ejpam-6985	91	3	2.3	2.3	NUM
ejpam-6985	91	4	)	)	PUNCT
ejpam-6985	91	5	and	and	CCONJ
ejpam-6985	91	6	integration	integration	NOUN
ejpam-6985	91	7	by	by	ADP
ejpam-6985	91	8	parts	part	NOUN
ejpam-6985	91	9	,	,	PUNCT
ejpam-6985	91	10	one	one	PRON
ejpam-6985	91	11	finds	find	VERB
ejpam-6985	91	12	|du|h(m	|du|h(m	NOUN
ejpam-6985	91	13	)	)	PUNCT
ejpam-6985	91	14	≤	≤	NUM
ejpam-6985	91	15	∫	∫	PROPN
ejpam-6985	91	16	m	m	PROPN
ejpam-6985	91	17	|∇bu|	|∇bu|	PROPN
ejpam-6985	91	18	dµ.	dµ.	NOUN
ejpam-6985	91	19	the	the	DET
ejpam-6985	91	20	reverse	reverse	ADJ
ejpam-6985	91	21	inequality	inequality	NOUN
ejpam-6985	91	22	is	be	AUX
ejpam-6985	91	23	obtained	obtain	VERB
ejpam-6985	91	24	by	by	ADP
ejpam-6985	91	25	testing	test	VERB
ejpam-6985	91	26	with	with	ADP
ejpam-6985	91	27	vector	vector	NOUN
ejpam-6985	91	28	fields	field	NOUN
ejpam-6985	91	29	aligned	align	VERB
ejpam-6985	91	30	with	with	ADP
ejpam-6985	91	31	−∇bu/|∇bu|	−∇bu/|∇bu|	NOUN
ejpam-6985	91	32	on	on	ADP
ejpam-6985	91	33	the	the	DET
ejpam-6985	91	34	set	set	NOUN
ejpam-6985	91	35	where	where	SCONJ
ejpam-6985	91	36	|∇bu|	|∇bu|	X
ejpam-6985	91	37	>	>	X
ejpam-6985	91	38	ε	ε	PROPN
ejpam-6985	91	39	and	and	CCONJ
ejpam-6985	91	40	letting	let	VERB
ejpam-6985	91	41	ε→	ε→	NOUN
ejpam-6985	91	42	0	0	NUM
ejpam-6985	91	43	.	.	PUNCT
ejpam-6985	92	1	hence	hence	ADV
ejpam-6985	92	2	(	(	PUNCT
ejpam-6985	92	3	2.5	2.5	NUM
ejpam-6985	92	4	)	)	PUNCT
ejpam-6985	92	5	holds	hold	VERB
ejpam-6985	92	6	.	.	PUNCT
ejpam-6985	93	1	the	the	DET
ejpam-6985	93	2	proof	proof	NOUN
ejpam-6985	93	3	is	be	AUX
ejpam-6985	93	4	complete	complete	ADJ
ejpam-6985	93	5	.	.	PUNCT
ejpam-6985	94	1	a.	a.	PROPN
ejpam-6985	94	2	ben	ben	PROPN
ejpam-6985	94	3	ahmed	ahmed	PROPN
ejpam-6985	94	4	/	/	SYM
ejpam-6985	94	5	eur	eur	PROPN
ejpam-6985	94	6	.	.	PUNCT
ejpam-6985	95	1	j.	j.	PROPN
ejpam-6985	95	2	pure	pure	PROPN
ejpam-6985	95	3	appl	appl	PROPN
ejpam-6985	95	4	.	.	PROPN
ejpam-6985	95	5	math	math	PROPN
ejpam-6985	95	6	,	,	PUNCT
ejpam-6985	95	7	18	18	NUM
ejpam-6985	95	8	(	(	PUNCT
ejpam-6985	95	9	4	4	NUM
ejpam-6985	95	10	)	)	PUNCT
ejpam-6985	95	11	(	(	PUNCT
ejpam-6985	95	12	2025	2025	NUM
ejpam-6985	95	13	)	)	PUNCT
ejpam-6985	95	14	,	,	PUNCT
ejpam-6985	95	15	6985	6985	NUM
ejpam-6985	95	16	5	5	NUM
ejpam-6985	95	17	of	of	ADP
ejpam-6985	95	18	16	16	NUM
ejpam-6985	95	19	2.3	2.3	NUM
ejpam-6985	95	20	.	.	PUNCT
ejpam-6985	96	1	isoperimetric	isoperimetric	ADJ
ejpam-6985	96	2	and	and	CCONJ
ejpam-6985	96	3	functional	functional	ADJ
ejpam-6985	96	4	inequalities	inequality	NOUN
ejpam-6985	96	5	we	we	PRON
ejpam-6985	96	6	will	will	AUX
ejpam-6985	96	7	rely	rely	VERB
ejpam-6985	96	8	on	on	ADP
ejpam-6985	96	9	isoperimetric	isoperimetric	ADJ
ejpam-6985	96	10	and	and	CCONJ
ejpam-6985	96	11	poincaré	poincaré	ADJ
ejpam-6985	96	12	inequalities	inequality	NOUN
ejpam-6985	96	13	available	available	ADJ
ejpam-6985	96	14	in	in	ADP
ejpam-6985	96	15	strictly	strictly	ADV
ejpam-6985	96	16	pseudoconvex	pseudoconvex	PROPN
ejpam-6985	96	17	cr	cr	PROPN
ejpam-6985	96	18	manifolds	manifold	NOUN
ejpam-6985	96	19	under	under	ADP
ejpam-6985	96	20	mild	mild	ADJ
ejpam-6985	96	21	quantitative	quantitative	ADJ
ejpam-6985	96	22	controls	control	NOUN
ejpam-6985	96	23	(	(	PUNCT
ejpam-6985	96	24	volume	volume	NOUN
ejpam-6985	96	25	doubling	doubling	NOUN
ejpam-6985	96	26	,	,	PUNCT
ejpam-6985	96	27	cc	cc	NOUN
ejpam-6985	96	28	-	-	NOUN
ejpam-6985	96	29	diameter	diameter	NOUN
ejpam-6985	96	30	bounds	bound	NOUN
ejpam-6985	96	31	,	,	PUNCT
ejpam-6985	96	32	or	or	CCONJ
ejpam-6985	96	33	curvature	curvature	NOUN
ejpam-6985	96	34	-	-	PUNCT
ejpam-6985	96	35	dimension	dimension	NOUN
ejpam-6985	96	36	assumptions	assumption	NOUN
ejpam-6985	96	37	)	)	PUNCT
ejpam-6985	96	38	.	.	PUNCT
ejpam-6985	97	1	we	we	PRON
ejpam-6985	97	2	state	state	VERB
ejpam-6985	97	3	them	they	PRON
ejpam-6985	97	4	in	in	ADP
ejpam-6985	97	5	a	a	DET
ejpam-6985	97	6	form	form	NOUN
ejpam-6985	97	7	convenient	convenient	ADJ
ejpam-6985	97	8	for	for	ADP
ejpam-6985	97	9	our	our	PRON
ejpam-6985	97	10	spectral	spectral	ADJ
ejpam-6985	97	11	estimates	estimate	NOUN
ejpam-6985	97	12	;	;	PUNCT
ejpam-6985	97	13	precise	precise	ADJ
ejpam-6985	97	14	constants	constant	NOUN
ejpam-6985	97	15	depend	depend	VERB
ejpam-6985	97	16	on	on	ADP
ejpam-6985	97	17	the	the	DET
ejpam-6985	97	18	chosen	choose	VERB
ejpam-6985	97	19	normalization	normalization	NOUN
ejpam-6985	97	20	and	and	CCONJ
ejpam-6985	97	21	on	on	ADP
ejpam-6985	97	22	geometric	geometric	ADJ
ejpam-6985	97	23	bounds	bound	NOUN
ejpam-6985	97	24	(	(	PUNCT
ejpam-6985	97	25	torsion	torsion	NOUN
ejpam-6985	97	26	,	,	PUNCT
ejpam-6985	97	27	lower	low	ADJ
ejpam-6985	97	28	horizontal	horizontal	ADJ
ejpam-6985	97	29	ricci	ricci	PROPN
ejpam-6985	97	30	)	)	PUNCT
ejpam-6985	97	31	.	.	PUNCT
ejpam-6985	98	1	proposition	proposition	NOUN
ejpam-6985	98	2	2	2	NUM
ejpam-6985	98	3	(	(	PUNCT
ejpam-6985	98	4	horizontal	horizontal	ADJ
ejpam-6985	98	5	isoperimetric	isoperimetric	ADJ
ejpam-6985	98	6	inequality	inequality	NOUN
ejpam-6985	98	7	)	)	PUNCT
ejpam-6985	98	8	.	.	PUNCT
ejpam-6985	99	1	let	let	VERB
ejpam-6985	99	2	(	(	PUNCT
ejpam-6985	99	3	m	m	NOUN
ejpam-6985	99	4	,	,	PUNCT
ejpam-6985	99	5	θ	θ	PROPN
ejpam-6985	99	6	,	,	PUNCT
ejpam-6985	99	7	j	j	NOUN
ejpam-6985	99	8	)	)	PUNCT
ejpam-6985	99	9	be	be	VERB
ejpam-6985	99	10	a	a	DET
ejpam-6985	99	11	compact	compact	ADJ
ejpam-6985	99	12	strictly	strictly	ADV
ejpam-6985	99	13	pseudoconvex	pseudoconvex	VERB
ejpam-6985	99	14	pseudo	pseudo	NOUN
ejpam-6985	99	15	-	-	ADJ
ejpam-6985	99	16	hermitian	hermitian	ADJ
ejpam-6985	99	17	cr	cr	PROPN
ejpam-6985	99	18	manifold	manifold	ADJ
ejpam-6985	99	19	and	and	CCONJ
ejpam-6985	99	20	let	let	VERB
ejpam-6985	99	21	q	q	NOUN
ejpam-6985	99	22	=	=	SYM
ejpam-6985	99	23	2n+	2n+	NUM
ejpam-6985	99	24	2	2	NUM
ejpam-6985	99	25	denote	denote	VERB
ejpam-6985	99	26	its	its	PRON
ejpam-6985	99	27	homogeneous	homogeneous	ADJ
ejpam-6985	99	28	dimension	dimension	NOUN
ejpam-6985	99	29	.	.	PUNCT
ejpam-6985	100	1	then	then	ADV
ejpam-6985	100	2	there	there	PRON
ejpam-6985	100	3	exists	exist	VERB
ejpam-6985	100	4	a	a	DET
ejpam-6985	100	5	constant	constant	ADJ
ejpam-6985	100	6	ciso	ciso	NOUN
ejpam-6985	100	7	>	>	X
ejpam-6985	100	8	0	0	NUM
ejpam-6985	100	9	,	,	PUNCT
ejpam-6985	100	10	depending	depend	VERB
ejpam-6985	100	11	only	only	ADV
ejpam-6985	100	12	on	on	ADP
ejpam-6985	100	13	q	q	ADJ
ejpam-6985	100	14	and	and	CCONJ
ejpam-6985	100	15	quantitative	quantitative	ADJ
ejpam-6985	100	16	pseudo	pseudo	NOUN
ejpam-6985	100	17	-	-	ADJ
ejpam-6985	100	18	hermitian	hermitian	ADJ
ejpam-6985	100	19	bounds	bound	NOUN
ejpam-6985	100	20	,	,	PUNCT
ejpam-6985	100	21	such	such	ADJ
ejpam-6985	100	22	that	that	PRON
ejpam-6985	100	23	for	for	ADP
ejpam-6985	100	24	every	every	DET
ejpam-6985	100	25	measurable	measurable	ADJ
ejpam-6985	100	26	set	set	NOUN
ejpam-6985	100	27	e	e	SYM
ejpam-6985	100	28	⊂m	⊂m	PROPN
ejpam-6985	100	29	with	with	ADP
ejpam-6985	100	30	µ(e	µ(e	PROPN
ejpam-6985	100	31	)	)	PUNCT
ejpam-6985	100	32	≤	≤	NUM
ejpam-6985	100	33	1	1	NUM
ejpam-6985	100	34	2µ(m	2µ(m	NUM
ejpam-6985	100	35	)	)	PUNCT
ejpam-6985	100	36	one	one	NOUN
ejpam-6985	100	37	has	have	VERB
ejpam-6985	100	38	µ(e	µ(e	PROPN
ejpam-6985	100	39	)	)	PUNCT
ejpam-6985	101	1	q−1	q−1	PROPN
ejpam-6985	101	2	q	q	PROPN
ejpam-6985	101	3	≤	≤	NUM
ejpam-6985	101	4	ciso	ciso	PROPN
ejpam-6985	101	5	perh(e;m	perh(e;m	VERB
ejpam-6985	101	6	)	)	PUNCT
ejpam-6985	101	7	,	,	PUNCT
ejpam-6985	101	8	(	(	PUNCT
ejpam-6985	101	9	2.6	2.6	NUM
ejpam-6985	101	10	)	)	PUNCT
ejpam-6985	101	11	where	where	SCONJ
ejpam-6985	101	12	µ	µ	NOUN
ejpam-6985	101	13	is	be	AUX
ejpam-6985	101	14	the	the	DET
ejpam-6985	101	15	pseudo	pseudo	NOUN
ejpam-6985	101	16	-	-	ADJ
ejpam-6985	101	17	hermitian	hermitian	ADJ
ejpam-6985	101	18	volume	volume	NOUN
ejpam-6985	101	19	and	and	CCONJ
ejpam-6985	101	20	perh(e;m	perh(e;m	VERB
ejpam-6985	101	21	)	)	PUNCT
ejpam-6985	101	22	the	the	DET
ejpam-6985	101	23	horizontal	horizontal	ADJ
ejpam-6985	101	24	perimeter	perimeter	NOUN
ejpam-6985	101	25	.	.	PUNCT
ejpam-6985	102	1	proof	proof	NOUN
ejpam-6985	102	2	.	.	PUNCT
ejpam-6985	103	1	the	the	DET
ejpam-6985	103	2	inequality	inequality	NOUN
ejpam-6985	103	3	is	be	AUX
ejpam-6985	103	4	the	the	DET
ejpam-6985	103	5	cr	cr	PROPN
ejpam-6985	103	6	analogue	analogue	NOUN
ejpam-6985	103	7	of	of	ADP
ejpam-6985	103	8	the	the	DET
ejpam-6985	103	9	classical	classical	ADJ
ejpam-6985	103	10	isoperimetric	isoperimetric	ADJ
ejpam-6985	103	11	inequality	inequality	NOUN
ejpam-6985	103	12	in	in	ADP
ejpam-6985	103	13	euclidean	euclidean	NOUN
ejpam-6985	103	14	and	and	CCONJ
ejpam-6985	103	15	carnot	carnot	NOUN
ejpam-6985	103	16	–	–	PUNCT
ejpam-6985	103	17	carathéodory	carathéodory	NOUN
ejpam-6985	103	18	geometries	geometry	NOUN
ejpam-6985	103	19	.	.	PUNCT
ejpam-6985	104	1	we	we	PRON
ejpam-6985	104	2	proceed	proceed	VERB
ejpam-6985	104	3	in	in	ADP
ejpam-6985	104	4	three	three	NUM
ejpam-6985	104	5	steps	step	NOUN
ejpam-6985	104	6	.	.	PUNCT
ejpam-6985	105	1	step	step	NOUN
ejpam-6985	105	2	1	1	NUM
ejpam-6985	105	3	:	:	PUNCT
ejpam-6985	105	4	model	model	NOUN
ejpam-6985	105	5	case	case	NOUN
ejpam-6985	105	6	on	on	ADP
ejpam-6985	105	7	the	the	DET
ejpam-6985	105	8	heisenberg	heisenberg	PROPN
ejpam-6985	105	9	group	group	NOUN
ejpam-6985	105	10	.	.	PUNCT
ejpam-6985	106	1	on	on	ADP
ejpam-6985	106	2	the	the	DET
ejpam-6985	106	3	heisenberg	heisenberg	PROPN
ejpam-6985	106	4	group	group	NOUN
ejpam-6985	106	5	hn	hn	PROPN
ejpam-6985	106	6	with	with	ADP
ejpam-6985	106	7	its	its	PRON
ejpam-6985	106	8	standard	standard	ADJ
ejpam-6985	106	9	cr	cr	PROPN
ejpam-6985	106	10	structure	structure	NOUN
ejpam-6985	106	11	,	,	PUNCT
ejpam-6985	106	12	the	the	DET
ejpam-6985	106	13	sharp	sharp	ADJ
ejpam-6985	106	14	isoperimetric	isoperimetric	ADJ
ejpam-6985	106	15	inequality	inequality	NOUN
ejpam-6985	106	16	is	be	AUX
ejpam-6985	106	17	known	know	VERB
ejpam-6985	106	18	:	:	PUNCT
ejpam-6985	106	19	|e|	|e|	PRON
ejpam-6985	106	20	q−1	q−1	PROPN
ejpam-6985	106	21	q	q	PROPN
ejpam-6985	106	22	≤	≤	PROPN
ejpam-6985	106	23	c	c	NOUN
ejpam-6985	106	24	perh(e	perh(e	PROPN
ejpam-6985	106	25	)	)	PUNCT
ejpam-6985	106	26	,	,	PUNCT
ejpam-6985	107	1	∀e	∀e	PROPN
ejpam-6985	107	2	⊂	⊂	PROPN
ejpam-6985	107	3	hn	hn	PROPN
ejpam-6985	107	4	,	,	PUNCT
ejpam-6985	107	5	where	where	SCONJ
ejpam-6985	107	6	|	|	ADV
ejpam-6985	107	7	·	·	PUNCT
ejpam-6985	107	8	|	|	ADV
ejpam-6985	107	9	denotes	denote	VERB
ejpam-6985	107	10	haar	haar	NOUN
ejpam-6985	107	11	measure	measure	NOUN
ejpam-6985	107	12	and	and	CCONJ
ejpam-6985	107	13	perh	perh	VERB
ejpam-6985	107	14	the	the	DET
ejpam-6985	107	15	horizontal	horizontal	ADJ
ejpam-6985	107	16	perimeter	perimeter	NOUN
ejpam-6985	107	17	.	.	PUNCT
ejpam-6985	108	1	this	this	DET
ejpam-6985	108	2	result	result	NOUN
ejpam-6985	108	3	goes	go	VERB
ejpam-6985	108	4	back	back	ADV
ejpam-6985	108	5	to	to	ADP
ejpam-6985	108	6	pansu	pansu	VERB
ejpam-6985	108	7	and	and	CCONJ
ejpam-6985	108	8	was	be	AUX
ejpam-6985	108	9	rigorously	rigorously	ADV
ejpam-6985	108	10	established	establish	VERB
ejpam-6985	108	11	in	in	ADP
ejpam-6985	108	12	[	[	X
ejpam-6985	108	13	7	7	NUM
ejpam-6985	108	14	,	,	PUNCT
ejpam-6985	108	15	9	9	NUM
ejpam-6985	108	16	]	]	PUNCT
ejpam-6985	108	17	.	.	PUNCT
ejpam-6985	109	1	the	the	DET
ejpam-6985	109	2	sharp	sharp	ADJ
ejpam-6985	109	3	constant	constant	ADJ
ejpam-6985	109	4	c	c	NOUN
ejpam-6985	109	5	depends	depend	VERB
ejpam-6985	109	6	only	only	ADV
ejpam-6985	109	7	on	on	ADP
ejpam-6985	109	8	n.	n.	NOUN
ejpam-6985	109	9	step	step	NOUN
ejpam-6985	109	10	2	2	NUM
ejpam-6985	109	11	:	:	PUNCT
ejpam-6985	109	12	local	local	ADJ
ejpam-6985	109	13	comparison	comparison	NOUN
ejpam-6985	109	14	on	on	ADP
ejpam-6985	109	15	cr	cr	PROPN
ejpam-6985	109	16	manifolds	manifolds	PROPN
ejpam-6985	109	17	.	.	PUNCT
ejpam-6985	110	1	in	in	ADP
ejpam-6985	110	2	a	a	DET
ejpam-6985	110	3	strictly	strictly	ADV
ejpam-6985	110	4	pseudoconvex	pseudoconvex	PROPN
ejpam-6985	110	5	cr	cr	PROPN
ejpam-6985	110	6	manifold	manifold	PROPN
ejpam-6985	110	7	(	(	PUNCT
ejpam-6985	110	8	m	m	PROPN
ejpam-6985	110	9	,	,	PUNCT
ejpam-6985	110	10	θ	θ	PROPN
ejpam-6985	110	11	,	,	PUNCT
ejpam-6985	110	12	j	j	NOUN
ejpam-6985	110	13	)	)	PUNCT
ejpam-6985	110	14	,	,	PUNCT
ejpam-6985	110	15	privileged	privileged	ADJ
ejpam-6985	110	16	coordinates	coordinate	NOUN
ejpam-6985	110	17	(	(	PUNCT
ejpam-6985	110	18	in	in	ADP
ejpam-6985	110	19	the	the	DET
ejpam-6985	110	20	sense	sense	NOUN
ejpam-6985	110	21	of	of	ADP
ejpam-6985	110	22	rothschild	rothschild	PROPN
ejpam-6985	110	23	–	–	PUNCT
ejpam-6985	110	24	stein	stein	PROPN
ejpam-6985	110	25	)	)	PUNCT
ejpam-6985	110	26	allow	allow	VERB
ejpam-6985	110	27	comparison	comparison	NOUN
ejpam-6985	110	28	between	between	ADP
ejpam-6985	110	29	small	small	ADJ
ejpam-6985	110	30	carnot	carnot	NOUN
ejpam-6985	110	31	–	–	PUNCT
ejpam-6985	110	32	carathéodory	carathéodory	NOUN
ejpam-6985	110	33	(	(	PUNCT
ejpam-6985	110	34	cc	cc	NOUN
ejpam-6985	110	35	)	)	PUNCT
ejpam-6985	110	36	balls	ball	NOUN
ejpam-6985	110	37	in	in	ADP
ejpam-6985	110	38	m	m	NOUN
ejpam-6985	110	39	and	and	CCONJ
ejpam-6985	110	40	balls	ball	NOUN
ejpam-6985	110	41	in	in	ADP
ejpam-6985	110	42	hn	hn	PROPN
ejpam-6985	110	43	.	.	PUNCT
ejpam-6985	111	1	more	more	ADV
ejpam-6985	111	2	precisely	precisely	ADV
ejpam-6985	111	3	,	,	PUNCT
ejpam-6985	111	4	under	under	ADP
ejpam-6985	111	5	uniform	uniform	ADJ
ejpam-6985	111	6	bounds	bound	NOUN
ejpam-6985	111	7	on	on	ADP
ejpam-6985	111	8	the	the	DET
ejpam-6985	111	9	pseudo	pseudo	NOUN
ejpam-6985	111	10	-	-	ADJ
ejpam-6985	111	11	hermitian	hermitian	ADJ
ejpam-6985	111	12	structure	structure	NOUN
ejpam-6985	111	13	(	(	PUNCT
ejpam-6985	111	14	torsion	torsion	NOUN
ejpam-6985	111	15	,	,	PUNCT
ejpam-6985	111	16	curvature	curvature	NOUN
ejpam-6985	111	17	and	and	CCONJ
ejpam-6985	111	18	injectivity	injectivity	NOUN
ejpam-6985	111	19	radius	radius	NOUN
ejpam-6985	111	20	)	)	PUNCT
ejpam-6985	111	21	,	,	PUNCT
ejpam-6985	111	22	small	small	ADJ
ejpam-6985	111	23	cc	cc	NOUN
ejpam-6985	111	24	balls	ball	NOUN
ejpam-6985	111	25	are	be	AUX
ejpam-6985	111	26	quantitatively	quantitatively	ADV
ejpam-6985	111	27	close	close	ADJ
ejpam-6985	111	28	—	—	PUNCT
ejpam-6985	111	29	in	in	ADP
ejpam-6985	111	30	both	both	CCONJ
ejpam-6985	111	31	metric	metric	ADJ
ejpam-6985	111	32	and	and	CCONJ
ejpam-6985	111	33	measure	measure	NOUN
ejpam-6985	111	34	—	—	PUNCT
ejpam-6985	111	35	to	to	ADP
ejpam-6985	111	36	heisenberg	heisenberg	PROPN
ejpam-6985	111	37	balls	ball	NOUN
ejpam-6985	111	38	.	.	PUNCT
ejpam-6985	112	1	consequently	consequently	ADV
ejpam-6985	112	2	,	,	PUNCT
ejpam-6985	112	3	relative	relative	ADJ
ejpam-6985	112	4	isoperimetric	isoperimetric	ADJ
ejpam-6985	112	5	inequalities	inequality	NOUN
ejpam-6985	112	6	valid	valid	ADJ
ejpam-6985	112	7	in	in	ADP
ejpam-6985	112	8	hn	hn	PROPN
ejpam-6985	112	9	transfer	transfer	NOUN
ejpam-6985	112	10	locally	locally	ADV
ejpam-6985	112	11	to	to	ADP
ejpam-6985	112	12	m	m	PROPN
ejpam-6985	112	13	with	with	ADP
ejpam-6985	112	14	controlled	control	VERB
ejpam-6985	112	15	constants	constant	NOUN
ejpam-6985	112	16	(	(	PUNCT
ejpam-6985	112	17	see	see	VERB
ejpam-6985	112	18	[	[	X
ejpam-6985	112	19	6	6	NUM
ejpam-6985	112	20	,	,	PUNCT
ejpam-6985	112	21	7	7	NUM
ejpam-6985	112	22	]	]	NUM
ejpam-6985	112	23	)	)	PUNCT
ejpam-6985	112	24	.	.	PUNCT
ejpam-6985	113	1	step	step	NOUN
ejpam-6985	113	2	3	3	NUM
ejpam-6985	113	3	:	:	PUNCT
ejpam-6985	113	4	globalization	globalization	NOUN
ejpam-6985	113	5	.	.	PUNCT
ejpam-6985	114	1	cover	cover	VERB
ejpam-6985	114	2	m	m	VERB
ejpam-6985	114	3	by	by	ADP
ejpam-6985	114	4	finitely	finitely	ADV
ejpam-6985	114	5	many	many	ADJ
ejpam-6985	114	6	cc	cc	ADP
ejpam-6985	114	7	balls	ball	NOUN
ejpam-6985	114	8	of	of	ADP
ejpam-6985	114	9	small	small	ADJ
ejpam-6985	114	10	radius	radius	NOUN
ejpam-6985	114	11	.	.	PUNCT
ejpam-6985	115	1	the	the	DET
ejpam-6985	115	2	relative	relative	ADJ
ejpam-6985	115	3	isoperimetric	isoperimetric	ADJ
ejpam-6985	115	4	inequality	inequality	NOUN
ejpam-6985	115	5	in	in	ADP
ejpam-6985	115	6	each	each	DET
ejpam-6985	115	7	ball	ball	NOUN
ejpam-6985	115	8	,	,	PUNCT
ejpam-6985	115	9	together	together	ADV
ejpam-6985	115	10	with	with	ADP
ejpam-6985	115	11	a	a	DET
ejpam-6985	115	12	partition	partition	NOUN
ejpam-6985	115	13	-	-	PUNCT
ejpam-6985	115	14	of	of	ADP
ejpam-6985	115	15	-	-	PUNCT
ejpam-6985	115	16	unity	unity	NOUN
ejpam-6985	115	17	and	and	CCONJ
ejpam-6985	115	18	a	a	DET
ejpam-6985	115	19	standard	standard	ADJ
ejpam-6985	115	20	compactness	compactness	NOUN
ejpam-6985	115	21	argument	argument	NOUN
ejpam-6985	115	22	,	,	PUNCT
ejpam-6985	115	23	yields	yield	VERB
ejpam-6985	115	24	a	a	DET
ejpam-6985	115	25	global	global	ADJ
ejpam-6985	115	26	inequality	inequality	NOUN
ejpam-6985	115	27	of	of	ADP
ejpam-6985	115	28	the	the	DET
ejpam-6985	115	29	form	form	NOUN
ejpam-6985	115	30	min{µ(e	min{µ(e	PROPN
ejpam-6985	115	31	)	)	PUNCT
ejpam-6985	115	32	,	,	PUNCT
ejpam-6985	115	33	µ(m	µ(m	PROPN
ejpam-6985	115	34	\	\	X
ejpam-6985	115	35	e	e	NOUN
ejpam-6985	115	36	)	)	PUNCT
ejpam-6985	115	37	}	}	PUNCT
ejpam-6985	116	1	q−1	q−1	PROPN
ejpam-6985	116	2	q	q	PROPN
ejpam-6985	116	3	≤	≤	NUM
ejpam-6985	116	4	ciso	ciso	NOUN
ejpam-6985	116	5	perh(e;m	perh(e;m	VERB
ejpam-6985	116	6	)	)	PUNCT
ejpam-6985	116	7	,	,	PUNCT
ejpam-6985	116	8	valid	valid	ADJ
ejpam-6985	116	9	for	for	ADP
ejpam-6985	116	10	all	all	DET
ejpam-6985	116	11	measurable	measurable	ADJ
ejpam-6985	116	12	e	e	X
ejpam-6985	116	13	⊂m	⊂m	PROPN
ejpam-6985	116	14	.	.	PUNCT
ejpam-6985	117	1	restricting	restrict	VERB
ejpam-6985	117	2	to	to	ADP
ejpam-6985	117	3	µ(e	µ(e	PROPN
ejpam-6985	117	4	)	)	PUNCT
ejpam-6985	117	5	≤	≤	NUM
ejpam-6985	117	6	1	1	NUM
ejpam-6985	117	7	2µ(m	2µ(m	NUM
ejpam-6985	117	8	)	)	PUNCT
ejpam-6985	117	9	gives	give	VERB
ejpam-6985	117	10	(	(	PUNCT
ejpam-6985	117	11	2.6	2.6	NUM
ejpam-6985	117	12	)	)	PUNCT
ejpam-6985	117	13	.	.	PUNCT
ejpam-6985	118	1	thus	thus	ADV
ejpam-6985	118	2	the	the	DET
ejpam-6985	118	3	horizontal	horizontal	ADJ
ejpam-6985	118	4	isoperimetric	isoperimetric	ADJ
ejpam-6985	118	5	inequality	inequality	NOUN
ejpam-6985	118	6	(	(	PUNCT
ejpam-6985	118	7	2.6	2.6	NUM
ejpam-6985	118	8	)	)	PUNCT
ejpam-6985	118	9	holds	hold	VERB
ejpam-6985	118	10	with	with	ADP
ejpam-6985	118	11	a	a	DET
ejpam-6985	118	12	constant	constant	ADJ
ejpam-6985	118	13	ciso	ciso	NOUN
ejpam-6985	118	14	depending	depend	VERB
ejpam-6985	118	15	only	only	ADV
ejpam-6985	118	16	on	on	ADP
ejpam-6985	118	17	q	q	NOUN
ejpam-6985	118	18	and	and	CCONJ
ejpam-6985	118	19	on	on	ADP
ejpam-6985	118	20	quantitative	quantitative	ADJ
ejpam-6985	118	21	bounds	bound	NOUN
ejpam-6985	118	22	of	of	ADP
ejpam-6985	118	23	the	the	DET
ejpam-6985	118	24	pseudo	pseudo	NOUN
ejpam-6985	118	25	-	-	ADJ
ejpam-6985	118	26	hermitian	hermitian	ADJ
ejpam-6985	118	27	structure	structure	NOUN
ejpam-6985	118	28	.	.	PUNCT
ejpam-6985	119	1	a.	a.	PROPN
ejpam-6985	119	2	ben	ben	PROPN
ejpam-6985	119	3	ahmed	ahmed	PROPN
ejpam-6985	119	4	/	/	SYM
ejpam-6985	119	5	eur	eur	PROPN
ejpam-6985	119	6	.	.	PUNCT
ejpam-6985	120	1	j.	j.	PROPN
ejpam-6985	120	2	pure	pure	PROPN
ejpam-6985	120	3	appl	appl	PROPN
ejpam-6985	120	4	.	.	PROPN
ejpam-6985	120	5	math	math	PROPN
ejpam-6985	120	6	,	,	PUNCT
ejpam-6985	120	7	18	18	NUM
ejpam-6985	120	8	(	(	PUNCT
ejpam-6985	120	9	4	4	NUM
ejpam-6985	120	10	)	)	PUNCT
ejpam-6985	120	11	(	(	PUNCT
ejpam-6985	120	12	2025	2025	NUM
ejpam-6985	120	13	)	)	PUNCT
ejpam-6985	120	14	,	,	PUNCT
ejpam-6985	120	15	6985	6985	NUM
ejpam-6985	120	16	6	6	NUM
ejpam-6985	120	17	of	of	ADP
ejpam-6985	120	18	16	16	NUM
ejpam-6985	120	19	proposition	proposition	NOUN
ejpam-6985	120	20	3	3	NUM
ejpam-6985	120	21	(	(	PUNCT
ejpam-6985	120	22	horizontal	horizontal	ADJ
ejpam-6985	120	23	poincaré	poincaré	ADJ
ejpam-6985	120	24	inequality	inequality	NOUN
ejpam-6985	120	25	)	)	PUNCT
ejpam-6985	120	26	.	.	PUNCT
ejpam-6985	121	1	let	let	VERB
ejpam-6985	121	2	(	(	PUNCT
ejpam-6985	121	3	m	m	PROPN
ejpam-6985	121	4	,	,	PUNCT
ejpam-6985	121	5	dcc	dcc	PROPN
ejpam-6985	121	6	,	,	PUNCT
ejpam-6985	121	7	µ	µ	X
ejpam-6985	121	8	)	)	PUNCT
ejpam-6985	121	9	be	be	VERB
ejpam-6985	121	10	a	a	DET
ejpam-6985	121	11	compact	compact	ADJ
ejpam-6985	121	12	pseudohermitian	pseudohermitian	ADJ
ejpam-6985	121	13	manifold	manifold	NOUN
ejpam-6985	121	14	with	with	ADP
ejpam-6985	121	15	bounded	bounded	ADJ
ejpam-6985	121	16	carnot	carnot	NOUN
ejpam-6985	121	17	–	–	PUNCT
ejpam-6985	121	18	carathéodory	carathéodory	NOUN
ejpam-6985	121	19	diameter	diameter	NOUN
ejpam-6985	121	20	diamcc(m	diamcc(m	PROPN
ejpam-6985	121	21	)	)	PUNCT
ejpam-6985	121	22	<	<	X
ejpam-6985	121	23	∞	∞	PROPN
ejpam-6985	121	24	,	,	PUNCT
ejpam-6985	121	25	and	and	CCONJ
ejpam-6985	121	26	assume	assume	VERB
ejpam-6985	121	27	that	that	SCONJ
ejpam-6985	121	28	m	m	NOUN
ejpam-6985	121	29	satisfies	satisfy	VERB
ejpam-6985	121	30	the	the	DET
ejpam-6985	121	31	local	local	ADJ
ejpam-6985	121	32	doubling	double	VERB
ejpam-6985	121	33	property	property	NOUN
ejpam-6985	121	34	and	and	CCONJ
ejpam-6985	121	35	a	a	DET
ejpam-6985	121	36	local	local	ADJ
ejpam-6985	121	37	poincaré	poincaré	ADJ
ejpam-6985	121	38	inequality	inequality	NOUN
ejpam-6985	121	39	.	.	PUNCT
ejpam-6985	122	1	then	then	ADV
ejpam-6985	122	2	there	there	PRON
ejpam-6985	122	3	exists	exist	VERB
ejpam-6985	122	4	a	a	DET
ejpam-6985	122	5	constant	constant	ADJ
ejpam-6985	122	6	cp	cp	INTJ
ejpam-6985	122	7	>	>	X
ejpam-6985	122	8	0	0	NUM
ejpam-6985	122	9	such	such	ADJ
ejpam-6985	122	10	that	that	PRON
ejpam-6985	122	11	for	for	SCONJ
ejpam-6985	122	12	every	every	DET
ejpam-6985	122	13	lipschitz	lipschitz	NOUN
ejpam-6985	122	14	function	function	NOUN
ejpam-6985	122	15	u	u	NOUN
ejpam-6985	122	16	with	with	ADP
ejpam-6985	122	17	vanishing	vanish	VERB
ejpam-6985	122	18	average	average	ADJ
ejpam-6985	122	19	∫	∫	PROPN
ejpam-6985	122	20	m	m	VERB
ejpam-6985	122	21	u	u	NOUN
ejpam-6985	122	22	dµ	dµ	ADJ
ejpam-6985	122	23	=	=	SYM
ejpam-6985	122	24	0	0	PROPN
ejpam-6985	122	25	,	,	PUNCT
ejpam-6985	122	26	one	one	NUM
ejpam-6985	122	27	has∫	has∫	NOUN
ejpam-6985	122	28	m	m	VERB
ejpam-6985	122	29	|u|	|u|	PROPN
ejpam-6985	122	30	dµ	dµ	ADJ
ejpam-6985	122	31	≤	≤	ADJ
ejpam-6985	122	32	cp	cp	NUM
ejpam-6985	122	33	diamcc(m	diamcc(m	PROPN
ejpam-6985	122	34	)	)	PUNCT
ejpam-6985	122	35	∫	∫	PROPN
ejpam-6985	122	36	m	m	PROPN
ejpam-6985	122	37	|∇bu|	|∇bu|	PROPN
ejpam-6985	122	38	dµ.	dµ.	PROPN
ejpam-6985	122	39	(	(	PUNCT
ejpam-6985	122	40	2.7	2.7	NUM
ejpam-6985	122	41	)	)	PUNCT
ejpam-6985	122	42	proof	proof	NOUN
ejpam-6985	122	43	.	.	PUNCT
ejpam-6985	123	1	standard	standard	NOUN
ejpam-6985	123	2	from	from	ADP
ejpam-6985	123	3	the	the	DET
ejpam-6985	123	4	(	(	PUNCT
ejpam-6985	123	5	1,1)-poincaré	1,1)-poincaré	NUM
ejpam-6985	123	6	inequality	inequality	NOUN
ejpam-6985	123	7	in	in	ADP
ejpam-6985	123	8	the	the	DET
ejpam-6985	123	9	carnot	carnot	NOUN
ejpam-6985	123	10	–	–	PUNCT
ejpam-6985	123	11	carathéodory	carathéodory	NOUN
ejpam-6985	123	12	setting	setting	NOUN
ejpam-6985	123	13	and	and	CCONJ
ejpam-6985	123	14	the	the	DET
ejpam-6985	123	15	fact	fact	NOUN
ejpam-6985	123	16	that	that	SCONJ
ejpam-6985	123	17	m	m	NOUN
ejpam-6985	123	18	is	be	AUX
ejpam-6985	123	19	compact	compact	ADJ
ejpam-6985	123	20	;	;	PUNCT
ejpam-6985	123	21	see	see	VERB
ejpam-6985	123	22	[	[	X
ejpam-6985	123	23	4	4	NUM
ejpam-6985	123	24	,	,	PUNCT
ejpam-6985	123	25	7	7	NUM
ejpam-6985	123	26	,	,	PUNCT
ejpam-6985	123	27	13	13	NUM
ejpam-6985	123	28	]	]	PUNCT
ejpam-6985	123	29	.	.	PUNCT
ejpam-6985	124	1	remark	remark	PROPN
ejpam-6985	124	2	1	1	NUM
ejpam-6985	124	3	.	.	PUNCT
ejpam-6985	125	1	all	all	DET
ejpam-6985	125	2	constants	constant	NOUN
ejpam-6985	125	3	ciso	ciso	PROPN
ejpam-6985	125	4	,	,	PUNCT
ejpam-6985	125	5	cp	cp	PROPN
ejpam-6985	125	6	can	can	AUX
ejpam-6985	125	7	be	be	AUX
ejpam-6985	125	8	made	make	VERB
ejpam-6985	125	9	explicit	explicit	ADJ
ejpam-6985	125	10	once	once	SCONJ
ejpam-6985	125	11	one	one	NUM
ejpam-6985	125	12	fixes	fix	NOUN
ejpam-6985	125	13	quantitative	quantitative	ADJ
ejpam-6985	125	14	bounds	bound	NOUN
ejpam-6985	125	15	on	on	ADP
ejpam-6985	125	16	torsion	torsion	NOUN
ejpam-6985	125	17	,	,	PUNCT
ejpam-6985	125	18	horizontal	horizontal	ADJ
ejpam-6985	125	19	ricci	ricci	NOUN
ejpam-6985	125	20	-	-	PUNCT
ejpam-6985	125	21	like	like	ADJ
ejpam-6985	125	22	quantities	quantity	NOUN
ejpam-6985	125	23	(	(	PUNCT
ejpam-6985	125	24	via	via	ADP
ejpam-6985	125	25	curvature	curvature	NOUN
ejpam-6985	125	26	-	-	PUNCT
ejpam-6985	125	27	dimension	dimension	NOUN
ejpam-6985	125	28	inequalities	inequality	NOUN
ejpam-6985	125	29	)	)	PUNCT
ejpam-6985	125	30	and	and	CCONJ
ejpam-6985	125	31	the	the	DET
ejpam-6985	125	32	carnot	carnot	NOUN
ejpam-6985	125	33	–	–	PUNCT
ejpam-6985	125	34	carathéodory	carathéodory	NOUN
ejpam-6985	125	35	diameter	diameter	NOUN
ejpam-6985	125	36	.	.	PUNCT
ejpam-6985	126	1	later	later	ADV
ejpam-6985	126	2	we	we	PRON
ejpam-6985	126	3	will	will	AUX
ejpam-6985	126	4	express	express	VERB
ejpam-6985	126	5	the	the	DET
ejpam-6985	126	6	dependence	dependence	NOUN
ejpam-6985	126	7	of	of	ADP
ejpam-6985	126	8	spectral	spectral	ADJ
ejpam-6985	126	9	constants	constant	NOUN
ejpam-6985	126	10	on	on	ADP
ejpam-6985	126	11	these	these	DET
ejpam-6985	126	12	geometric	geometric	ADJ
ejpam-6985	126	13	data	datum	NOUN
ejpam-6985	126	14	.	.	PUNCT
ejpam-6985	127	1	3	3	X
ejpam-6985	127	2	.	.	X
ejpam-6985	127	3	the	the	DET
ejpam-6985	127	4	cr	cr	PROPN
ejpam-6985	127	5	cheeger	cheeger	ADV
ejpam-6985	127	6	constant	constant	ADJ
ejpam-6985	127	7	and	and	CCONJ
ejpam-6985	127	8	main	main	ADJ
ejpam-6985	127	9	theorem	theorem	ADJ
ejpam-6985	127	10	definition	definition	NOUN
ejpam-6985	127	11	1	1	NUM
ejpam-6985	127	12	(	(	PUNCT
ejpam-6985	127	13	cr	cr	NOUN
ejpam-6985	127	14	cheeger	cheeger	ADV
ejpam-6985	127	15	constant	constant	ADJ
ejpam-6985	127	16	)	)	PUNCT
ejpam-6985	127	17	.	.	PUNCT
ejpam-6985	128	1	let	let	AUX
ejpam-6985	128	2	(	(	PUNCT
ejpam-6985	128	3	m	m	NOUN
ejpam-6985	128	4	,	,	PUNCT
ejpam-6985	128	5	θ	θ	PROPN
ejpam-6985	128	6	,	,	PUNCT
ejpam-6985	128	7	j	j	NOUN
ejpam-6985	128	8	)	)	PUNCT
ejpam-6985	128	9	be	be	AUX
ejpam-6985	128	10	compact	compact	ADJ
ejpam-6985	128	11	strictly	strictly	ADV
ejpam-6985	128	12	pseudoconvex	pseudoconvex	PROPN
ejpam-6985	128	13	cr	cr	PROPN
ejpam-6985	128	14	manifold	manifold	PROPN
ejpam-6985	128	15	.	.	PUNCT
ejpam-6985	129	1	the	the	DET
ejpam-6985	129	2	cr	cr	PROPN
ejpam-6985	129	3	cheeger	cheeger	ADV
ejpam-6985	129	4	constant	constant	ADJ
ejpam-6985	129	5	is	be	AUX
ejpam-6985	129	6	hcr(m	hcr(m	ADV
ejpam-6985	129	7	)	)	PUNCT
ejpam-6985	129	8	:	:	PUNCT
ejpam-6985	129	9	=	=	SYM
ejpam-6985	129	10	inf	inf	PROPN
ejpam-6985	129	11	e⊂m	e⊂m	NOUN
ejpam-6985	129	12	perh(e;m	perh(e;m	VERB
ejpam-6985	129	13	)	)	PUNCT
ejpam-6985	129	14	min{µ(e	min{µ(e	PROPN
ejpam-6985	129	15	)	)	PUNCT
ejpam-6985	129	16	,	,	PUNCT
ejpam-6985	129	17	µ(m	µ(m	PROPN
ejpam-6985	129	18	\	\	X
ejpam-6985	129	19	e	e	NOUN
ejpam-6985	129	20	)	)	PUNCT
ejpam-6985	129	21	}	}	PUNCT
ejpam-6985	129	22	,	,	PUNCT
ejpam-6985	129	23	(	(	PUNCT
ejpam-6985	129	24	3.1	3.1	NUM
ejpam-6985	129	25	)	)	PUNCT
ejpam-6985	129	26	infimum	infimum	NOUN
ejpam-6985	129	27	taken	take	VERB
ejpam-6985	129	28	over	over	ADP
ejpam-6985	129	29	sets	set	NOUN
ejpam-6985	129	30	of	of	ADP
ejpam-6985	129	31	finite	finite	PROPN
ejpam-6985	129	32	horizontal	horizontal	PROPN
ejpam-6985	129	33	perimeter	perimeter	PROPN
ejpam-6985	129	34	.	.	PUNCT
ejpam-6985	130	1	our	our	PRON
ejpam-6985	130	2	main	main	ADJ
ejpam-6985	130	3	spectral	spectral	ADJ
ejpam-6985	130	4	result	result	NOUN
ejpam-6985	130	5	is	be	AUX
ejpam-6985	130	6	the	the	DET
ejpam-6985	130	7	following	following	NOUN
ejpam-6985	130	8	.	.	PUNCT
ejpam-6985	131	1	theorem	theorem	ADJ
ejpam-6985	131	2	1	1	NUM
ejpam-6985	131	3	(	(	PUNCT
ejpam-6985	131	4	cheeger	cheeger	ADV
ejpam-6985	131	5	–	–	PUNCT
ejpam-6985	131	6	cr	cr	PRON
ejpam-6985	131	7	inequality	inequality	NOUN
ejpam-6985	131	8	)	)	PUNCT
ejpam-6985	131	9	.	.	PUNCT
ejpam-6985	132	1	let	let	VERB
ejpam-6985	132	2	(	(	PUNCT
ejpam-6985	132	3	m	m	NOUN
ejpam-6985	132	4	,	,	PUNCT
ejpam-6985	132	5	θ	θ	PROPN
ejpam-6985	132	6	,	,	PUNCT
ejpam-6985	132	7	j	j	NOUN
ejpam-6985	132	8	)	)	PUNCT
ejpam-6985	132	9	be	be	VERB
ejpam-6985	132	10	a	a	DET
ejpam-6985	132	11	compact	compact	ADJ
ejpam-6985	132	12	strictly	strictly	ADV
ejpam-6985	132	13	pseudoconvex	pseudoconvex	VERB
ejpam-6985	132	14	pseudo	pseudo	NOUN
ejpam-6985	132	15	-	-	ADJ
ejpam-6985	132	16	hermitian	hermitian	ADJ
ejpam-6985	132	17	cr	cr	PROPN
ejpam-6985	132	18	manifold	manifold	PROPN
ejpam-6985	132	19	.	.	PUNCT
ejpam-6985	133	1	denote	denote	VERB
ejpam-6985	133	2	by	by	ADP
ejpam-6985	133	3	λ1	λ1	PROPN
ejpam-6985	133	4	=	=	SYM
ejpam-6985	133	5	λ1(∆b	λ1(∆b	PROPN
ejpam-6985	133	6	)	)	PUNCT
ejpam-6985	133	7	the	the	DET
ejpam-6985	133	8	first	first	ADJ
ejpam-6985	133	9	positive	positive	ADJ
ejpam-6985	133	10	eigenvalue	eigenvalue	NOUN
ejpam-6985	133	11	of	of	ADP
ejpam-6985	133	12	the	the	DET
ejpam-6985	133	13	sub	sub	ADJ
ejpam-6985	133	14	-	-	ADJ
ejpam-6985	133	15	laplacian	laplacian	ADJ
ejpam-6985	133	16	∆b	∆b	PROPN
ejpam-6985	133	17	on	on	ADP
ejpam-6985	133	18	functions	function	NOUN
ejpam-6985	133	19	(	(	PUNCT
ejpam-6985	133	20	with	with	ADP
ejpam-6985	133	21	respect	respect	NOUN
ejpam-6985	133	22	to	to	ADP
ejpam-6985	133	23	the	the	DET
ejpam-6985	133	24	measure	measure	NOUN
ejpam-6985	133	25	µ	µ	NOUN
ejpam-6985	133	26	)	)	PUNCT
ejpam-6985	133	27	.	.	PUNCT
ejpam-6985	134	1	then	then	ADV
ejpam-6985	134	2	λ1	λ1	PROPN
ejpam-6985	134	3	≥	≥	PROPN
ejpam-6985	134	4	c∗(q	c∗(q	PROPN
ejpam-6985	134	5	,	,	PUNCT
ejpam-6985	134	6	t	t	PROPN
ejpam-6985	134	7	)	)	PUNCT
ejpam-6985	134	8	hcr(m)2	hcr(m)2	NOUN
ejpam-6985	134	9	,	,	PUNCT
ejpam-6985	134	10	(	(	PUNCT
ejpam-6985	134	11	3.2	3.2	NUM
ejpam-6985	134	12	)	)	PUNCT
ejpam-6985	135	1	where	where	SCONJ
ejpam-6985	135	2	q	q	NOUN
ejpam-6985	136	1	=	=	SYM
ejpam-6985	137	1	2n+	2n+	NUM
ejpam-6985	137	2	2	2	NUM
ejpam-6985	137	3	and	and	CCONJ
ejpam-6985	137	4	c∗(q	c∗(q	PROPN
ejpam-6985	137	5	,	,	PUNCT
ejpam-6985	137	6	t	t	PROPN
ejpam-6985	137	7	)	)	PUNCT
ejpam-6985	137	8	∈	∈	PROPN
ejpam-6985	137	9	(	(	PUNCT
ejpam-6985	137	10	0	0	NUM
ejpam-6985	137	11	,	,	PUNCT
ejpam-6985	137	12	14	14	NUM
ejpam-6985	137	13	]	]	PUNCT
ejpam-6985	137	14	is	be	AUX
ejpam-6985	137	15	an	an	DET
ejpam-6985	137	16	explicit	explicit	ADJ
ejpam-6985	137	17	constant	constant	ADJ
ejpam-6985	137	18	depending	depend	VERB
ejpam-6985	137	19	only	only	ADV
ejpam-6985	137	20	on	on	ADP
ejpam-6985	137	21	q	q	PROPN
ejpam-6985	137	22	and	and	CCONJ
ejpam-6985	137	23	controlled	control	VERB
ejpam-6985	137	24	pseudo	pseudo	NOUN
ejpam-6985	137	25	-	-	ADJ
ejpam-6985	137	26	hermitian	hermitian	ADJ
ejpam-6985	137	27	bounds	bound	NOUN
ejpam-6985	137	28	t.	t.	PROPN
ejpam-6985	137	29	in	in	ADP
ejpam-6985	137	30	torsion	torsion	NOUN
ejpam-6985	137	31	-	-	PUNCT
ejpam-6985	137	32	free	free	ADJ
ejpam-6985	137	33	model	model	NOUN
ejpam-6985	137	34	settings	setting	NOUN
ejpam-6985	137	35	(	(	PUNCT
ejpam-6985	137	36	compact	compact	PROPN
ejpam-6985	137	37	heisenberg	heisenberg	PROPN
ejpam-6985	137	38	quotients	quotient	NOUN
ejpam-6985	137	39	,	,	PUNCT
ejpam-6985	137	40	standard	standard	ADJ
ejpam-6985	137	41	cr	cr	PROPN
ejpam-6985	137	42	sphere	sphere	ADV
ejpam-6985	137	43	)	)	PUNCT
ejpam-6985	137	44	one	one	PRON
ejpam-6985	137	45	can	can	AUX
ejpam-6985	137	46	take	take	VERB
ejpam-6985	137	47	c∗	c∗	NOUN
ejpam-6985	137	48	=	=	NOUN
ejpam-6985	137	49	1	1	NUM
ejpam-6985	137	50	4	4	NUM
ejpam-6985	137	51	under	under	ADP
ejpam-6985	137	52	the	the	DET
ejpam-6985	137	53	usual	usual	ADJ
ejpam-6985	137	54	normalization	normalization	NOUN
ejpam-6985	137	55	of	of	ADP
ejpam-6985	137	56	∆b	∆b	PROPN
ejpam-6985	137	57	.	.	PUNCT
ejpam-6985	137	58	proof	proof	NOUN
ejpam-6985	137	59	of	of	ADP
ejpam-6985	137	60	theorem	theorem	NOUN
ejpam-6985	137	61	1	1	NUM
ejpam-6985	137	62	the	the	DET
ejpam-6985	137	63	following	follow	VERB
ejpam-6985	137	64	propositions	proposition	NOUN
ejpam-6985	137	65	provide	provide	VERB
ejpam-6985	137	66	the	the	DET
ejpam-6985	137	67	key	key	ADJ
ejpam-6985	137	68	technical	technical	ADJ
ejpam-6985	137	69	ingredients	ingredient	NOUN
ejpam-6985	137	70	for	for	ADP
ejpam-6985	137	71	the	the	DET
ejpam-6985	137	72	proof	proof	NOUN
ejpam-6985	137	73	of	of	ADP
ejpam-6985	137	74	the	the	DET
ejpam-6985	137	75	main	main	ADJ
ejpam-6985	137	76	theorem	theorem	NOUN
ejpam-6985	137	77	.	.	PUNCT
ejpam-6985	138	1	a.	a.	PROPN
ejpam-6985	138	2	ben	ben	PROPN
ejpam-6985	138	3	ahmed	ahmed	PROPN
ejpam-6985	138	4	/	/	SYM
ejpam-6985	138	5	eur	eur	PROPN
ejpam-6985	138	6	.	.	PUNCT
ejpam-6985	139	1	j.	j.	PROPN
ejpam-6985	139	2	pure	pure	PROPN
ejpam-6985	139	3	appl	appl	PROPN
ejpam-6985	139	4	.	.	PROPN
ejpam-6985	139	5	math	math	PROPN
ejpam-6985	139	6	,	,	PUNCT
ejpam-6985	139	7	18	18	NUM
ejpam-6985	139	8	(	(	PUNCT
ejpam-6985	139	9	4	4	NUM
ejpam-6985	139	10	)	)	PUNCT
ejpam-6985	139	11	(	(	PUNCT
ejpam-6985	139	12	2025	2025	NUM
ejpam-6985	139	13	)	)	PUNCT
ejpam-6985	139	14	,	,	PUNCT
ejpam-6985	139	15	6985	6985	NUM
ejpam-6985	139	16	7	7	NUM
ejpam-6985	139	17	of	of	ADP
ejpam-6985	139	18	16	16	NUM
ejpam-6985	139	19	proposition	proposition	NOUN
ejpam-6985	139	20	4	4	NUM
ejpam-6985	139	21	(	(	PUNCT
ejpam-6985	139	22	cheeger	cheeger	ADV
ejpam-6985	139	23	slicing	slice	VERB
ejpam-6985	139	24	inequality	inequality	NOUN
ejpam-6985	139	25	,	,	PUNCT
ejpam-6985	139	26	horizontal	horizontal	ADJ
ejpam-6985	139	27	version	version	NOUN
ejpam-6985	139	28	)	)	PUNCT
ejpam-6985	139	29	.	.	PUNCT
ejpam-6985	140	1	let	let	VERB
ejpam-6985	140	2	f	f	PROPN
ejpam-6985	140	3	∈	∈	PROPN
ejpam-6985	140	4	lip(m	lip(m	PROPN
ejpam-6985	140	5	)	)	PUNCT
ejpam-6985	140	6	with∫	with∫	NOUN
ejpam-6985	140	7	m	m	NOUN
ejpam-6985	140	8	f	f	NOUN
ejpam-6985	140	9	dµ	dµ	PROPN
ejpam-6985	140	10	=	=	SYM
ejpam-6985	141	1	0	0	PROPN
ejpam-6985	141	2	.	.	PUNCT
ejpam-6985	142	1	then∫	then∫	NOUN
ejpam-6985	142	2	m	m	PROPN
ejpam-6985	142	3	|∇bf	|∇bf	PROPN
ejpam-6985	142	4	|	|	ADV
ejpam-6985	142	5	dµ	dµ	VERB
ejpam-6985	142	6	≥	≥	NOUN
ejpam-6985	142	7	hcr(m	hcr(m	ADV
ejpam-6985	142	8	)	)	PUNCT
ejpam-6985	142	9	∫	∫	PROPN
ejpam-6985	143	1	+	+	PROPN
ejpam-6985	143	2	∞	∞	PROPN
ejpam-6985	143	3	−∞	−∞	X
ejpam-6985	143	4	min{µ({f	min{µ({f	X
ejpam-6985	143	5	>	>	X
ejpam-6985	143	6	t	t	PROPN
ejpam-6985	143	7	}	}	PUNCT
ejpam-6985	143	8	)	)	PUNCT
ejpam-6985	143	9	,	,	PUNCT
ejpam-6985	143	10	µ({f	µ({f	VERB
ejpam-6985	143	11	≤	≤	PROPN
ejpam-6985	143	12	t	t	PROPN
ejpam-6985	143	13	}	}	PUNCT
ejpam-6985	143	14	)	)	PUNCT
ejpam-6985	143	15	}	}	PUNCT
ejpam-6985	144	1	dt	dt	PROPN
ejpam-6985	144	2	.	.	PUNCT
ejpam-6985	145	1	(	(	PUNCT
ejpam-6985	145	2	3.3	3.3	NUM
ejpam-6985	145	3	)	)	PUNCT
ejpam-6985	145	4	consequently	consequently	ADV
ejpam-6985	145	5	,	,	PUNCT
ejpam-6985	145	6	there	there	PRON
ejpam-6985	145	7	exists	exist	VERB
ejpam-6985	145	8	t0	t0	PROPN
ejpam-6985	145	9	∈	∈	PROPN
ejpam-6985	145	10	r	r	NOUN
ejpam-6985	145	11	such	such	ADJ
ejpam-6985	145	12	that∫	that∫	NOUN
ejpam-6985	145	13	m	m	PROPN
ejpam-6985	145	14	|∇bf	|∇bf	PROPN
ejpam-6985	145	15	|	|	ADV
ejpam-6985	145	16	dµ	dµ	VERB
ejpam-6985	145	17	≥	≥	NOUN
ejpam-6985	145	18	1	1	NUM
ejpam-6985	145	19	2	2	NUM
ejpam-6985	145	20	hcr(m	hcr(m	NOUN
ejpam-6985	145	21	)	)	PUNCT
ejpam-6985	145	22	∫	∫	PROPN
ejpam-6985	145	23	m	m	PROPN
ejpam-6985	145	24	|f	|f	PROPN
ejpam-6985	146	1	|	|	PROPN
ejpam-6985	146	2	dµ.	dµ.	PROPN
ejpam-6985	146	3	(	(	PUNCT
ejpam-6985	146	4	3.4	3.4	NUM
ejpam-6985	146	5	)	)	PUNCT
ejpam-6985	146	6	proof	proof	NOUN
ejpam-6985	146	7	.	.	PUNCT
ejpam-6985	146	8	apply	apply	VERB
ejpam-6985	146	9	the	the	DET
ejpam-6985	146	10	horizontal	horizontal	ADJ
ejpam-6985	146	11	co	co	NOUN
ejpam-6985	146	12	-	-	NOUN
ejpam-6985	146	13	area	area	NOUN
ejpam-6985	146	14	formula	formula	NOUN
ejpam-6985	146	15	(	(	PUNCT
ejpam-6985	146	16	proposition	proposition	NOUN
ejpam-6985	146	17	1	1	NUM
ejpam-6985	146	18	)	)	PUNCT
ejpam-6985	146	19	to	to	ADP
ejpam-6985	146	20	f	f	PROPN
ejpam-6985	146	21	:	:	PUNCT
ejpam-6985	146	22	∫	∫	PROPN
ejpam-6985	146	23	m	m	PROPN
ejpam-6985	146	24	|∇bf	|∇bf	PROPN
ejpam-6985	146	25	|	|	ADV
ejpam-6985	146	26	dµ	dµ	VERB
ejpam-6985	146	27	=	=	SYM
ejpam-6985	146	28	∫	∫	PROPN
ejpam-6985	146	29	∞	∞	PROPN
ejpam-6985	147	1	−∞	−∞	ADP
ejpam-6985	147	2	perh({f	perh({f	PROPN
ejpam-6985	147	3	>	>	PUNCT
ejpam-6985	147	4	t};m	t};m	PROPN
ejpam-6985	147	5	)	)	PUNCT
ejpam-6985	147	6	dt	dt	NOUN
ejpam-6985	147	7	.	.	PUNCT
ejpam-6985	148	1	by	by	ADP
ejpam-6985	148	2	definition	definition	NOUN
ejpam-6985	148	3	of	of	ADP
ejpam-6985	148	4	hcr(m	hcr(m	PROPN
ejpam-6985	148	5	)	)	PUNCT
ejpam-6985	148	6	,	,	PUNCT
ejpam-6985	148	7	perh({f	perh({f	PROPN
ejpam-6985	148	8	>	>	PUNCT
ejpam-6985	148	9	t};m	t};m	PROPN
ejpam-6985	148	10	)	)	PUNCT
ejpam-6985	148	11	≥	≥	NOUN
ejpam-6985	148	12	hcr(m	hcr(m	NOUN
ejpam-6985	148	13	)	)	PUNCT
ejpam-6985	148	14	min{µ({f	min{µ({f	X
ejpam-6985	148	15	>	>	X
ejpam-6985	148	16	t	t	PROPN
ejpam-6985	148	17	}	}	PUNCT
ejpam-6985	148	18	)	)	PUNCT
ejpam-6985	148	19	,	,	PUNCT
ejpam-6985	148	20	µ({f	µ({f	VERB
ejpam-6985	148	21	≤	≤	PROPN
ejpam-6985	148	22	t	t	PROPN
ejpam-6985	148	23	}	}	PUNCT
ejpam-6985	148	24	)	)	PUNCT
ejpam-6985	148	25	}	}	PUNCT
ejpam-6985	148	26	.	.	PUNCT
ejpam-6985	149	1	integrate	integrate	VERB
ejpam-6985	149	2	in	in	ADP
ejpam-6985	149	3	t	t	PROPN
ejpam-6985	149	4	to	to	PART
ejpam-6985	149	5	obtain	obtain	VERB
ejpam-6985	149	6	(	(	PUNCT
ejpam-6985	149	7	3.3	3.3	NUM
ejpam-6985	149	8	)	)	PUNCT
ejpam-6985	149	9	.	.	PUNCT
ejpam-6985	150	1	the	the	DET
ejpam-6985	150	2	identity∫	identity∫	ADJ
ejpam-6985	150	3	∞	∞	PROPN
ejpam-6985	150	4	−∞	−∞	X
ejpam-6985	150	5	min{µ({f	min{µ({f	X
ejpam-6985	150	6	>	>	X
ejpam-6985	150	7	t	t	PROPN
ejpam-6985	150	8	}	}	PUNCT
ejpam-6985	150	9	)	)	PUNCT
ejpam-6985	150	10	,	,	PUNCT
ejpam-6985	150	11	µ({f	µ({f	VERB
ejpam-6985	150	12	≤	≤	PROPN
ejpam-6985	150	13	t	t	PROPN
ejpam-6985	150	14	}	}	PUNCT
ejpam-6985	150	15	)	)	PUNCT
ejpam-6985	150	16	}	}	PUNCT
ejpam-6985	150	17	dt	dt	NOUN
ejpam-6985	151	1	=	=	SYM
ejpam-6985	151	2	1	1	NUM
ejpam-6985	151	3	2	2	NUM
ejpam-6985	151	4	∫	∫	NOUN
ejpam-6985	151	5	m	m	NOUN
ejpam-6985	151	6	|f	|f	PROPN
ejpam-6985	152	1	|	|	ADV
ejpam-6985	152	2	dµ	dµ	PRON
ejpam-6985	152	3	follows	follow	VERB
ejpam-6985	152	4	from	from	ADP
ejpam-6985	152	5	the	the	DET
ejpam-6985	152	6	cavalieri	cavalieri	PROPN
ejpam-6985	152	7	representation	representation	NOUN
ejpam-6985	152	8	applied	apply	VERB
ejpam-6985	152	9	to	to	ADP
ejpam-6985	152	10	|f	|f	PROPN
ejpam-6985	152	11	|	|	ADV
ejpam-6985	152	12	;	;	PUNCT
ejpam-6985	152	13	combining	combine	VERB
ejpam-6985	152	14	yields	yield	NOUN
ejpam-6985	152	15	(	(	PUNCT
ejpam-6985	152	16	3.4	3.4	NUM
ejpam-6985	152	17	)	)	PUNCT
ejpam-6985	152	18	.	.	PUNCT
ejpam-6985	153	1	proposition	proposition	NOUN
ejpam-6985	153	2	5	5	NUM
ejpam-6985	153	3	(	(	PUNCT
ejpam-6985	153	4	from	from	ADP
ejpam-6985	153	5	l1	l1	PROPN
ejpam-6985	153	6	control	control	NOUN
ejpam-6985	153	7	to	to	PART
ejpam-6985	153	8	l2	l2	VERB
ejpam-6985	153	9	estimate	estimate	NOUN
ejpam-6985	153	10	)	)	PUNCT
ejpam-6985	153	11	.	.	PUNCT
ejpam-6985	154	1	let	let	VERB
ejpam-6985	154	2	f	f	PROPN
ejpam-6985	154	3	∈	∈	PROPN
ejpam-6985	154	4	lip(m	lip(m	PROPN
ejpam-6985	154	5	)	)	PUNCT
ejpam-6985	154	6	with	with	ADP
ejpam-6985	154	7	∫	∫	PROPN
ejpam-6985	154	8	m	m	PROPN
ejpam-6985	154	9	f	f	PROPN
ejpam-6985	154	10	dµ	dµ	PROPN
ejpam-6985	154	11	=	=	SYM
ejpam-6985	155	1	0	0	X
ejpam-6985	155	2	.	.	PUNCT
ejpam-6985	156	1	then	then	ADV
ejpam-6985	156	2	∫	∫	PROPN
ejpam-6985	156	3	m	m	PROPN
ejpam-6985	156	4	|∇bf	|∇bf	PROPN
ejpam-6985	156	5	|2	|2	NUM
ejpam-6985	156	6	dµ	dµ	PRON
ejpam-6985	156	7	≥	≥	NOUN
ejpam-6985	156	8	hcr(m)2	hcr(m)2	VERB
ejpam-6985	156	9	4c2	4c2	NUM
ejpam-6985	156	10	pdiamcc(m)2	pdiamcc(m)2	NOUN
ejpam-6985	157	1	∫	∫	PROPN
ejpam-6985	157	2	m	m	PROPN
ejpam-6985	157	3	f2	f2	PROPN
ejpam-6985	157	4	dµ	dµ	PROPN
ejpam-6985	157	5	,	,	PUNCT
ejpam-6985	157	6	(	(	PUNCT
ejpam-6985	157	7	3.5	3.5	NUM
ejpam-6985	157	8	)	)	PUNCT
ejpam-6985	157	9	where	where	SCONJ
ejpam-6985	157	10	cp	cp	NOUN
ejpam-6985	157	11	and	and	CCONJ
ejpam-6985	157	12	diamcc(m	diamcc(m	PROPN
ejpam-6985	157	13	)	)	PUNCT
ejpam-6985	157	14	are	be	AUX
ejpam-6985	157	15	as	as	ADP
ejpam-6985	157	16	in	in	ADP
ejpam-6985	157	17	proposition	proposition	NOUN
ejpam-6985	157	18	3	3	NUM
ejpam-6985	157	19	.	.	PUNCT
ejpam-6985	158	1	in	in	ADP
ejpam-6985	158	2	particular	particular	ADJ
ejpam-6985	158	3	,	,	PUNCT
ejpam-6985	158	4	if	if	SCONJ
ejpam-6985	158	5	one	one	PRON
ejpam-6985	158	6	normalizes	normalize	VERB
ejpam-6985	158	7	so	so	SCONJ
ejpam-6985	158	8	that	that	DET
ejpam-6985	158	9	cpdiamcc(m	cpdiamcc(m	NOUN
ejpam-6985	158	10	)	)	PUNCT
ejpam-6985	158	11	=	=	PUNCT
ejpam-6985	159	1	1	1	NUM
ejpam-6985	159	2	then	then	ADV
ejpam-6985	159	3	the	the	DET
ejpam-6985	159	4	prefactor	prefactor	NOUN
ejpam-6985	159	5	is	be	AUX
ejpam-6985	159	6	hcr(m)2/4	hcr(m)2/4	PROPN
ejpam-6985	159	7	.	.	PUNCT
ejpam-6985	160	1	proof	proof	NOUN
ejpam-6985	160	2	.	.	PUNCT
ejpam-6985	161	1	from	from	ADP
ejpam-6985	161	2	proposition	proposition	NOUN
ejpam-6985	161	3	4	4	NUM
ejpam-6985	161	4	we	we	PRON
ejpam-6985	161	5	have∫	have∫	VERB
ejpam-6985	161	6	m	m	VERB
ejpam-6985	161	7	|∇bf	|∇bf	NOUN
ejpam-6985	161	8	|	|	ADV
ejpam-6985	161	9	dµ	dµ	VERB
ejpam-6985	161	10	≥	≥	NOUN
ejpam-6985	161	11	1	1	NUM
ejpam-6985	161	12	2hcr(m	2hcr(m	NUM
ejpam-6985	161	13	)	)	PUNCT
ejpam-6985	162	1	∫	∫	PROPN
ejpam-6985	163	1	m	m	PROPN
ejpam-6985	163	2	|f	|f	PROPN
ejpam-6985	164	1	|	|	ADV
ejpam-6985	164	2	dµ.	dµ.	VERB
ejpam-6985	164	3	by	by	ADP
ejpam-6985	164	4	the	the	DET
ejpam-6985	164	5	cauchy	cauchy	PROPN
ejpam-6985	164	6	–	–	PUNCT
ejpam-6985	164	7	schwarz	schwarz	PROPN
ejpam-6985	164	8	inequality,∫	inequality,∫	PROPN
ejpam-6985	164	9	m	m	PROPN
ejpam-6985	164	10	|∇bf	|∇bf	PROPN
ejpam-6985	164	11	|	|	ADV
ejpam-6985	164	12	dµ	dµ	VERB
ejpam-6985	164	13	≤	≤	NUM
ejpam-6985	164	14	(	(	PUNCT
ejpam-6985	164	15	∫	∫	PROPN
ejpam-6985	164	16	m	m	PROPN
ejpam-6985	164	17	|∇bf	|∇bf	PROPN
ejpam-6985	164	18	|2	|2	NUM
ejpam-6985	164	19	dµ	dµ	PROPN
ejpam-6985	164	20	)	)	PUNCT
ejpam-6985	164	21	1/2	1/2	NUM
ejpam-6985	164	22	µ(m)1/2	µ(m)1/2	NUM
ejpam-6985	164	23	,	,	PUNCT
ejpam-6985	164	24	and	and	CCONJ
ejpam-6985	164	25	by	by	ADP
ejpam-6985	164	26	proposition	proposition	NOUN
ejpam-6985	164	27	3	3	NUM
ejpam-6985	164	28	(	(	PUNCT
ejpam-6985	164	29	poincaré	poincaré	ADJ
ejpam-6985	164	30	with	with	ADP
ejpam-6985	164	31	zero	zero	NUM
ejpam-6985	164	32	mean)∫	mean)∫	X
ejpam-6985	165	1	m	m	PROPN
ejpam-6985	166	1	|f	|f	PROPN
ejpam-6985	167	1	|	|	ADV
ejpam-6985	167	2	dµ	dµ	VERB
ejpam-6985	167	3	≤	≤	NUM
ejpam-6985	167	4	cp	cp	NUM
ejpam-6985	167	5	diamcc(m	diamcc(m	PROPN
ejpam-6985	167	6	)	)	PUNCT
ejpam-6985	167	7	∫	∫	PROPN
ejpam-6985	167	8	m	m	PROPN
ejpam-6985	167	9	|∇bf	|∇bf	PROPN
ejpam-6985	167	10	|	|	ADV
ejpam-6985	167	11	dµ.	dµ.	VERB
ejpam-6985	167	12	a.	a.	PROPN
ejpam-6985	167	13	ben	ben	PROPN
ejpam-6985	167	14	ahmed	ahmed	PROPN
ejpam-6985	167	15	/	/	SYM
ejpam-6985	167	16	eur	eur	PROPN
ejpam-6985	167	17	.	.	PUNCT
ejpam-6985	168	1	j.	j.	PROPN
ejpam-6985	168	2	pure	pure	PROPN
ejpam-6985	168	3	appl	appl	PROPN
ejpam-6985	168	4	.	.	PROPN
ejpam-6985	168	5	math	math	PROPN
ejpam-6985	168	6	,	,	PUNCT
ejpam-6985	168	7	18	18	NUM
ejpam-6985	168	8	(	(	PUNCT
ejpam-6985	168	9	4	4	NUM
ejpam-6985	168	10	)	)	PUNCT
ejpam-6985	168	11	(	(	PUNCT
ejpam-6985	168	12	2025	2025	NUM
ejpam-6985	168	13	)	)	PUNCT
ejpam-6985	168	14	,	,	PUNCT
ejpam-6985	168	15	6985	6985	NUM
ejpam-6985	168	16	8	8	NUM
ejpam-6985	168	17	of	of	ADP
ejpam-6985	168	18	16	16	NUM
ejpam-6985	168	19	combining	combine	VERB
ejpam-6985	168	20	and	and	CCONJ
ejpam-6985	168	21	eliminating	eliminate	VERB
ejpam-6985	168	22	∫	∫	PROPN
ejpam-6985	168	23	m	m	PROPN
ejpam-6985	168	24	|∇bf	|∇bf	PROPN
ejpam-6985	168	25	|	|	ADV
ejpam-6985	168	26	dµ	dµ	VERB
ejpam-6985	168	27	yields(∫	yields(∫	PROPN
ejpam-6985	168	28	m	m	PROPN
ejpam-6985	168	29	|∇bf	|∇bf	PROPN
ejpam-6985	168	30	|2	|2	NUM
ejpam-6985	168	31	dµ	dµ	PROPN
ejpam-6985	168	32	)	)	PUNCT
ejpam-6985	168	33	1/2	1/2	NUM
ejpam-6985	168	34	≥	≥	NOUN
ejpam-6985	168	35	hcr(m	hcr(m	NOUN
ejpam-6985	168	36	)	)	PUNCT
ejpam-6985	168	37	2cpdiamcc(m	2cpdiamcc(m	NUM
ejpam-6985	168	38	)	)	PUNCT
ejpam-6985	168	39	(	(	PUNCT
ejpam-6985	168	40	∫	∫	PROPN
ejpam-6985	168	41	m	m	PROPN
ejpam-6985	168	42	f2	f2	PROPN
ejpam-6985	168	43	dµ	dµ	VERB
ejpam-6985	168	44	)	)	PUNCT
ejpam-6985	168	45	1/2	1/2	NUM
ejpam-6985	168	46	,	,	PUNCT
ejpam-6985	168	47	and	and	CCONJ
ejpam-6985	168	48	squaring	square	VERB
ejpam-6985	168	49	gives	give	NOUN
ejpam-6985	168	50	(	(	PUNCT
ejpam-6985	168	51	3.5	3.5	NUM
ejpam-6985	168	52	)	)	PUNCT
ejpam-6985	168	53	.	.	PUNCT
ejpam-6985	169	1	by	by	ADP
ejpam-6985	169	2	the	the	DET
ejpam-6985	169	3	rayleigh	rayleigh	PROPN
ejpam-6985	169	4	quotient	quotient	PROPN
ejpam-6985	169	5	characterization	characterization	NOUN
ejpam-6985	169	6	,	,	PUNCT
ejpam-6985	169	7	λ1	λ1	PROPN
ejpam-6985	169	8	=	=	PUNCT
ejpam-6985	169	9	inf	inf	PROPN
ejpam-6985	169	10	f∈c∞(m)∫	f∈c∞(m)∫	PROPN
ejpam-6985	169	11	f=0	f=0	PROPN
ejpam-6985	169	12	∫	∫	PROPN
ejpam-6985	169	13	m	m	PROPN
ejpam-6985	169	14	|∇bf	|∇bf	PROPN
ejpam-6985	169	15	|2	|2	NUM
ejpam-6985	169	16	dµ∫	dµ∫	PROPN
ejpam-6985	169	17	m	m	PROPN
ejpam-6985	169	18	f2	f2	ADJ
ejpam-6985	169	19	dµ	dµ	PROPN
ejpam-6985	169	20	.	.	PUNCT
ejpam-6985	170	1	applying	apply	VERB
ejpam-6985	170	2	proposition	proposition	NOUN
ejpam-6985	170	3	5	5	NUM
ejpam-6985	170	4	to	to	ADP
ejpam-6985	170	5	any	any	DET
ejpam-6985	170	6	admissible	admissible	ADJ
ejpam-6985	170	7	f	f	NOUN
ejpam-6985	170	8	yields	yield	NOUN
ejpam-6985	170	9	the	the	PRON
ejpam-6985	170	10	claimed	claim	VERB
ejpam-6985	170	11	lower	lower	ADV
ejpam-6985	170	12	bound	bind	VERB
ejpam-6985	170	13	with	with	ADP
ejpam-6985	170	14	c∗(q	c∗(q	PROPN
ejpam-6985	170	15	,	,	PUNCT
ejpam-6985	170	16	t	t	PROPN
ejpam-6985	170	17	)	)	PUNCT
ejpam-6985	170	18	=	=	SYM
ejpam-6985	170	19	1	1	NUM
ejpam-6985	170	20	4c2	4c2	NUM
ejpam-6985	170	21	pdiamcc(m)2	pdiamcc(m)2	NOUN
ejpam-6985	170	22	,	,	PUNCT
ejpam-6985	170	23	where	where	SCONJ
ejpam-6985	170	24	the	the	DET
ejpam-6985	170	25	dependence	dependence	NOUN
ejpam-6985	170	26	on	on	ADP
ejpam-6985	170	27	q	q	PROPN
ejpam-6985	170	28	and	and	CCONJ
ejpam-6985	170	29	t	t	PROPN
ejpam-6985	170	30	arises	arise	VERB
ejpam-6985	170	31	through	through	ADP
ejpam-6985	170	32	the	the	DET
ejpam-6985	170	33	poincaré	poincaré	ADJ
ejpam-6985	170	34	constant	constant	ADJ
ejpam-6985	170	35	cp	cp	NOUN
ejpam-6985	170	36	and	and	CCONJ
ejpam-6985	170	37	the	the	DET
ejpam-6985	170	38	diameter	diameter	NOUN
ejpam-6985	170	39	control	control	NOUN
ejpam-6985	170	40	(	(	PUNCT
ejpam-6985	170	41	both	both	PRON
ejpam-6985	170	42	of	of	ADP
ejpam-6985	170	43	which	which	PRON
ejpam-6985	170	44	can	can	AUX
ejpam-6985	170	45	be	be	AUX
ejpam-6985	170	46	quantified	quantify	VERB
ejpam-6985	170	47	under	under	ADP
ejpam-6985	170	48	curvature	curvature	NOUN
ejpam-6985	170	49	-	-	PUNCT
ejpam-6985	170	50	dimension	dimension	NOUN
ejpam-6985	170	51	or	or	CCONJ
ejpam-6985	170	52	torsion	torsion	NOUN
ejpam-6985	170	53	bounds	bound	NOUN
ejpam-6985	170	54	)	)	PUNCT
ejpam-6985	170	55	.	.	PUNCT
ejpam-6985	171	1	in	in	ADP
ejpam-6985	171	2	symmetric	symmetric	ADJ
ejpam-6985	171	3	torsion	torsion	NOUN
ejpam-6985	171	4	-	-	PUNCT
ejpam-6985	171	5	free	free	ADJ
ejpam-6985	171	6	models	model	NOUN
ejpam-6985	171	7	one	one	PRON
ejpam-6985	171	8	may	may	AUX
ejpam-6985	171	9	arrange	arrange	VERB
ejpam-6985	171	10	the	the	DET
ejpam-6985	171	11	normalization	normalization	NOUN
ejpam-6985	171	12	so	so	SCONJ
ejpam-6985	171	13	that	that	PRON
ejpam-6985	171	14	cpdiamcc(m	cpdiamcc(m	NOUN
ejpam-6985	171	15	)	)	PUNCT
ejpam-6985	171	16	=	=	SYM
ejpam-6985	171	17	1	1	NUM
ejpam-6985	171	18	,	,	PUNCT
ejpam-6985	171	19	recovering	recover	VERB
ejpam-6985	171	20	the	the	DET
ejpam-6985	171	21	classical	classical	ADJ
ejpam-6985	171	22	1/4	1/4	NUM
ejpam-6985	171	23	factor	factor	NOUN
ejpam-6985	171	24	.	.	PUNCT
ejpam-6985	172	1	this	this	PRON
ejpam-6985	172	2	completes	complete	VERB
ejpam-6985	172	3	the	the	DET
ejpam-6985	172	4	proof	proof	NOUN
ejpam-6985	172	5	of	of	ADP
ejpam-6985	172	6	theorem	theorem	ADJ
ejpam-6985	172	7	1	1	NUM
ejpam-6985	172	8	.	.	NOUN
ejpam-6985	172	9	remark	remark	NOUN
ejpam-6985	172	10	2	2	NUM
ejpam-6985	172	11	.	.	PUNCT
ejpam-6985	173	1	the	the	DET
ejpam-6985	173	2	chain	chain	NOUN
ejpam-6985	173	3	of	of	ADP
ejpam-6985	173	4	inequalities	inequality	NOUN
ejpam-6985	173	5	shows	show	VERB
ejpam-6985	173	6	precisely	precisely	ADV
ejpam-6985	173	7	where	where	SCONJ
ejpam-6985	173	8	pseudo	pseudo	NOUN
ejpam-6985	173	9	-	-	ADJ
ejpam-6985	173	10	hermitian	hermitian	ADJ
ejpam-6985	173	11	geometry	geometry	NOUN
ejpam-6985	173	12	enters	enter	VERB
ejpam-6985	173	13	:	:	PUNCT
ejpam-6985	173	14	the	the	DET
ejpam-6985	173	15	co	co	NOUN
ejpam-6985	173	16	-	-	NOUN
ejpam-6985	173	17	area	area	NOUN
ejpam-6985	173	18	formula	formula	NOUN
ejpam-6985	173	19	is	be	AUX
ejpam-6985	173	20	horizontal	horizontal	ADJ
ejpam-6985	173	21	,	,	PUNCT
ejpam-6985	173	22	the	the	DET
ejpam-6985	173	23	isoperimetric	isoperimetric	ADJ
ejpam-6985	173	24	profile	profile	NOUN
ejpam-6985	173	25	defines	define	VERB
ejpam-6985	173	26	hcr	hcr	NOUN
ejpam-6985	173	27	and	and	CCONJ
ejpam-6985	173	28	the	the	DET
ejpam-6985	173	29	poincaré	poincaré	ADJ
ejpam-6985	173	30	constant	constant	NOUN
ejpam-6985	173	31	depends	depend	VERB
ejpam-6985	173	32	on	on	ADP
ejpam-6985	173	33	doubling	double	VERB
ejpam-6985	173	34	and	and	CCONJ
ejpam-6985	173	35	curvature	curvature	NOUN
ejpam-6985	173	36	-	-	PUNCT
ejpam-6985	173	37	dimension	dimension	NOUN
ejpam-6985	173	38	assumptions	assumption	NOUN
ejpam-6985	173	39	that	that	PRON
ejpam-6985	173	40	may	may	AUX
ejpam-6985	173	41	involve	involve	VERB
ejpam-6985	173	42	webster	webster	PROPN
ejpam-6985	173	43	torsion	torsion	NOUN
ejpam-6985	173	44	.	.	PUNCT
ejpam-6985	174	1	hence	hence	ADV
ejpam-6985	174	2	explicit	explicit	ADJ
ejpam-6985	174	3	dependence	dependence	NOUN
ejpam-6985	174	4	of	of	ADP
ejpam-6985	174	5	c∗	c∗	NOUN
ejpam-6985	174	6	on	on	ADP
ejpam-6985	174	7	torsion	torsion	NOUN
ejpam-6985	174	8	can	can	AUX
ejpam-6985	174	9	be	be	AUX
ejpam-6985	174	10	tracked	track	VERB
ejpam-6985	174	11	by	by	ADP
ejpam-6985	174	12	quantifying	quantify	VERB
ejpam-6985	174	13	cp	cp	NUM
ejpam-6985	174	14	.	.	PUNCT
ejpam-6985	175	1	4	4	X
ejpam-6985	175	2	.	.	X
ejpam-6985	175	3	a	a	DET
ejpam-6985	175	4	conditional	conditional	ADJ
ejpam-6985	175	5	buser	buser	NOUN
ejpam-6985	175	6	–	–	PUNCT
ejpam-6985	175	7	cr	cr	PROPN
ejpam-6985	175	8	upper	upper	ADV
ejpam-6985	175	9	bound	bind	VERB
ejpam-6985	175	10	while	while	SCONJ
ejpam-6985	175	11	cheeger	cheeger	ADJ
ejpam-6985	175	12	-	-	PUNCT
ejpam-6985	175	13	type	type	NOUN
ejpam-6985	175	14	inequalities	inequality	NOUN
ejpam-6985	175	15	provide	provide	VERB
ejpam-6985	175	16	lower	low	ADJ
ejpam-6985	175	17	bounds	bound	NOUN
ejpam-6985	175	18	for	for	ADP
ejpam-6985	175	19	the	the	DET
ejpam-6985	175	20	first	first	ADJ
ejpam-6985	175	21	eigenvalue	eigenvalue	NOUN
ejpam-6985	175	22	of	of	ADP
ejpam-6985	175	23	the	the	DET
ejpam-6985	175	24	horizontal	horizontal	ADJ
ejpam-6985	175	25	sub	sub	ADJ
ejpam-6985	175	26	-	-	ADJ
ejpam-6985	175	27	laplacian	laplacian	ADJ
ejpam-6985	175	28	,	,	PUNCT
ejpam-6985	175	29	a	a	DET
ejpam-6985	175	30	converse	converse	NOUN
ejpam-6985	175	31	bound	bind	VERB
ejpam-6985	175	32	requires	require	VERB
ejpam-6985	175	33	stronger	strong	ADJ
ejpam-6985	175	34	analytic	analytic	ADJ
ejpam-6985	175	35	controls	control	NOUN
ejpam-6985	175	36	.	.	PUNCT
ejpam-6985	176	1	in	in	ADP
ejpam-6985	176	2	this	this	DET
ejpam-6985	176	3	section	section	NOUN
ejpam-6985	176	4	we	we	PRON
ejpam-6985	176	5	establish	establish	VERB
ejpam-6985	176	6	a	a	DET
ejpam-6985	176	7	cr	cr	NOUN
ejpam-6985	176	8	analogue	analogue	NOUN
ejpam-6985	176	9	of	of	ADP
ejpam-6985	176	10	buser	buser	PROPN
ejpam-6985	176	11	’s	’s	PART
ejpam-6985	176	12	inequality	inequality	NOUN
ejpam-6985	176	13	,	,	PUNCT
ejpam-6985	176	14	conditional	conditional	ADJ
ejpam-6985	176	15	on	on	ADP
ejpam-6985	176	16	standard	standard	ADJ
ejpam-6985	176	17	subriemannian	subriemannian	ADJ
ejpam-6985	176	18	analytic	analytic	ADJ
ejpam-6985	176	19	hypotheses	hypothesis	NOUN
ejpam-6985	176	20	.	.	PUNCT
ejpam-6985	177	1	the	the	DET
ejpam-6985	177	2	proof	proof	NOUN
ejpam-6985	177	3	adapts	adapt	VERB
ejpam-6985	177	4	buser	buser	NOUN
ejpam-6985	177	5	’s	’s	PART
ejpam-6985	177	6	variational	variational	ADJ
ejpam-6985	177	7	strategy	strategy	NOUN
ejpam-6985	177	8	to	to	ADP
ejpam-6985	177	9	the	the	DET
ejpam-6985	177	10	horizontal	horizontal	ADJ
ejpam-6985	177	11	distribution	distribution	NOUN
ejpam-6985	177	12	.	.	PUNCT
ejpam-6985	178	1	theorem	theorem	ADJ
ejpam-6985	178	2	2	2	NUM
ejpam-6985	178	3	(	(	PUNCT
ejpam-6985	178	4	buser	buser	NOUN
ejpam-6985	178	5	–	–	PUNCT
ejpam-6985	178	6	cr	cr	PROPN
ejpam-6985	178	7	inequality	inequality	NOUN
ejpam-6985	178	8	(	(	PUNCT
ejpam-6985	178	9	conditional	conditional	ADJ
ejpam-6985	178	10	)	)	PUNCT
ejpam-6985	178	11	)	)	PUNCT
ejpam-6985	178	12	.	.	PUNCT
ejpam-6985	179	1	let	let	VERB
ejpam-6985	179	2	(	(	PUNCT
ejpam-6985	179	3	m	m	NOUN
ejpam-6985	179	4	,	,	PUNCT
ejpam-6985	179	5	θ	θ	PROPN
ejpam-6985	179	6	,	,	PUNCT
ejpam-6985	179	7	j	j	NOUN
ejpam-6985	179	8	)	)	PUNCT
ejpam-6985	179	9	be	be	VERB
ejpam-6985	179	10	a	a	DET
ejpam-6985	179	11	compact	compact	ADJ
ejpam-6985	179	12	strictly	strictly	ADV
ejpam-6985	179	13	pseudoconvex	pseudoconvex	VERB
ejpam-6985	179	14	pseudo	pseudo	NOUN
ejpam-6985	179	15	-	-	ADJ
ejpam-6985	179	16	hermitian	hermitian	ADJ
ejpam-6985	179	17	cr	cr	PROPN
ejpam-6985	179	18	manifold	manifold	ADJ
ejpam-6985	179	19	and	and	CCONJ
ejpam-6985	179	20	let	let	VERB
ejpam-6985	179	21	∆b	∆b	PROPN
ejpam-6985	179	22	denote	denote	VERB
ejpam-6985	179	23	its	its	PRON
ejpam-6985	179	24	horizontal	horizontal	ADJ
ejpam-6985	179	25	sub	sub	NOUN
ejpam-6985	179	26	-	-	ADJ
ejpam-6985	179	27	laplacian	laplacian	ADJ
ejpam-6985	179	28	.	.	PUNCT
ejpam-6985	180	1	assume	assume	VERB
ejpam-6985	180	2	:	:	PUNCT
ejpam-6985	180	3	(	(	PUNCT
ejpam-6985	180	4	a1	a1	NOUN
ejpam-6985	180	5	)	)	PUNCT
ejpam-6985	180	6	(	(	PUNCT
ejpam-6985	180	7	m	m	PROPN
ejpam-6985	180	8	,	,	PUNCT
ejpam-6985	180	9	dcc	dcc	PROPN
ejpam-6985	180	10	,	,	PUNCT
ejpam-6985	180	11	µ	µ	X
ejpam-6985	180	12	)	)	PUNCT
ejpam-6985	180	13	satisfies	satisfy	VERB
ejpam-6985	180	14	a	a	DET
ejpam-6985	180	15	volume	volume	NOUN
ejpam-6985	180	16	doubling	double	VERB
ejpam-6985	180	17	property	property	NOUN
ejpam-6985	180	18	and	and	CCONJ
ejpam-6985	180	19	a	a	DET
ejpam-6985	180	20	(	(	PUNCT
ejpam-6985	180	21	1	1	NUM
ejpam-6985	180	22	,	,	PUNCT
ejpam-6985	180	23	1)-poincaré	1)-poincaré	NUM
ejpam-6985	180	24	inequality	inequality	NOUN
ejpam-6985	180	25	with	with	ADP
ejpam-6985	180	26	uniform	uniform	ADJ
ejpam-6985	180	27	constants	constant	NOUN
ejpam-6985	180	28	;	;	PUNCT
ejpam-6985	180	29	(	(	PUNCT
ejpam-6985	180	30	a2	a2	PROPN
ejpam-6985	180	31	)	)	PUNCT
ejpam-6985	180	32	the	the	DET
ejpam-6985	180	33	heat	heat	NOUN
ejpam-6985	180	34	kernel	kernel	PROPN
ejpam-6985	180	35	pt(x	pt(x	PROPN
ejpam-6985	180	36	,	,	PUNCT
ejpam-6985	180	37	y	y	NOUN
ejpam-6985	180	38	)	)	PUNCT
ejpam-6985	180	39	of	of	ADP
ejpam-6985	180	40	∆b	∆b	PROPN
ejpam-6985	180	41	satisfies	satisfie	NOUN
ejpam-6985	180	42	gaussian	gaussian	VERB
ejpam-6985	180	43	upper	upper	ADJ
ejpam-6985	180	44	bounds	bound	NOUN
ejpam-6985	180	45	:	:	PUNCT
ejpam-6985	180	46	there	there	PRON
ejpam-6985	180	47	exist	exist	VERB
ejpam-6985	180	48	a	a	DET
ejpam-6985	180	49	,	,	PUNCT
ejpam-6985	180	50	b	b	X
ejpam-6985	180	51	>	>	X
ejpam-6985	180	52	0	0	NUM
ejpam-6985	180	53	such	such	ADJ
ejpam-6985	180	54	that	that	SCONJ
ejpam-6985	180	55	pt(x	pt(x	PROPN
ejpam-6985	180	56	,	,	PUNCT
ejpam-6985	180	57	y	y	NOUN
ejpam-6985	180	58	)	)	PUNCT
ejpam-6985	180	59	≤	≤	NOUN
ejpam-6985	181	1	a	a	DET
ejpam-6985	181	2	µ(b(x	µ(b(x	PROPN
ejpam-6985	181	3	,	,	PUNCT
ejpam-6985	181	4	√	√	NUM
ejpam-6985	181	5	t	t	PROPN
ejpam-6985	181	6	)	)	PUNCT
ejpam-6985	181	7	)	)	PUNCT
ejpam-6985	181	8	exp	exp	NOUN
ejpam-6985	181	9	(	(	PUNCT
ejpam-6985	181	10	−	−	PROPN
ejpam-6985	181	11	dcc(x	dcc(x	PROPN
ejpam-6985	181	12	,	,	PUNCT
ejpam-6985	181	13	y	y	NOUN
ejpam-6985	181	14	)	)	PUNCT
ejpam-6985	181	15	2	2	NUM
ejpam-6985	181	16	bt	bt	NOUN
ejpam-6985	181	17	)	)	PUNCT
ejpam-6985	181	18	,	,	PUNCT
ejpam-6985	181	19	∀	∀	X
ejpam-6985	181	20	0	0	PUNCT
ejpam-6985	181	21	<	<	X
ejpam-6985	181	22	t	t	X
ejpam-6985	181	23	≤	≤	NUM
ejpam-6985	181	24	1	1	NUM
ejpam-6985	181	25	.	.	PUNCT
ejpam-6985	182	1	(	(	PUNCT
ejpam-6985	182	2	4.1	4.1	NUM
ejpam-6985	182	3	)	)	PUNCT
ejpam-6985	182	4	a.	a.	NOUN
ejpam-6985	182	5	ben	ben	PROPN
ejpam-6985	182	6	ahmed	ahmed	PROPN
ejpam-6985	182	7	/	/	SYM
ejpam-6985	182	8	eur	eur	PROPN
ejpam-6985	182	9	.	.	PUNCT
ejpam-6985	183	1	j.	j.	PROPN
ejpam-6985	183	2	pure	pure	PROPN
ejpam-6985	183	3	appl	appl	PROPN
ejpam-6985	183	4	.	.	PROPN
ejpam-6985	183	5	math	math	PROPN
ejpam-6985	183	6	,	,	PUNCT
ejpam-6985	183	7	18	18	NUM
ejpam-6985	183	8	(	(	PUNCT
ejpam-6985	183	9	4	4	NUM
ejpam-6985	183	10	)	)	PUNCT
ejpam-6985	183	11	(	(	PUNCT
ejpam-6985	183	12	2025	2025	NUM
ejpam-6985	183	13	)	)	PUNCT
ejpam-6985	183	14	,	,	PUNCT
ejpam-6985	183	15	6985	6985	NUM
ejpam-6985	183	16	9	9	NUM
ejpam-6985	183	17	of	of	ADP
ejpam-6985	183	18	16	16	NUM
ejpam-6985	183	19	then	then	ADV
ejpam-6985	183	20	there	there	PRON
ejpam-6985	183	21	exist	exist	VERB
ejpam-6985	183	22	constants	constant	NOUN
ejpam-6985	183	23	c1	c1	PROPN
ejpam-6985	183	24	,	,	PUNCT
ejpam-6985	183	25	c2	c2	PROPN
ejpam-6985	183	26	>	>	X
ejpam-6985	183	27	0	0	PROPN
ejpam-6985	183	28	,	,	PUNCT
ejpam-6985	183	29	depending	depend	VERB
ejpam-6985	183	30	only	only	ADV
ejpam-6985	183	31	on	on	ADP
ejpam-6985	183	32	the	the	DET
ejpam-6985	183	33	doubling	doubling	NOUN
ejpam-6985	183	34	,	,	PUNCT
ejpam-6985	183	35	poincaré	poincaré	ADJ
ejpam-6985	183	36	and	and	CCONJ
ejpam-6985	183	37	heat	heat	NOUN
ejpam-6985	183	38	-	-	PUNCT
ejpam-6985	183	39	kernel	kernel	NOUN
ejpam-6985	183	40	constants	constant	NOUN
ejpam-6985	183	41	,	,	PUNCT
ejpam-6985	184	1	such	such	ADJ
ejpam-6985	184	2	that	that	DET
ejpam-6985	184	3	λ1(∆b	λ1(∆b	NOUN
ejpam-6985	184	4	)	)	PUNCT
ejpam-6985	184	5	≤	≤	NUM
ejpam-6985	184	6	c1	c1	PROPN
ejpam-6985	184	7	hcr(m)2	hcr(m)2	VERB
ejpam-6985	184	8	+	+	CCONJ
ejpam-6985	184	9	c2	c2	PROPN
ejpam-6985	184	10	hcr(m	hcr(m	PROPN
ejpam-6985	184	11	)	)	PUNCT
ejpam-6985	184	12	,	,	PUNCT
ejpam-6985	184	13	(	(	PUNCT
ejpam-6985	184	14	4.2	4.2	NUM
ejpam-6985	184	15	)	)	PUNCT
ejpam-6985	184	16	where	where	SCONJ
ejpam-6985	184	17	hcr(m	hcr(m	X
ejpam-6985	184	18	)	)	PUNCT
ejpam-6985	184	19	is	be	AUX
ejpam-6985	184	20	the	the	DET
ejpam-6985	184	21	cr	cr	PROPN
ejpam-6985	184	22	cheeger	cheeger	ADV
ejpam-6985	184	23	constant	constant	ADJ
ejpam-6985	184	24	.	.	PUNCT
ejpam-6985	185	1	proof	proof	NOUN
ejpam-6985	185	2	of	of	ADP
ejpam-6985	185	3	theorem	theorem	NOUN
ejpam-6985	185	4	2	2	NUM
ejpam-6985	185	5	we	we	PRON
ejpam-6985	185	6	follow	follow	VERB
ejpam-6985	185	7	buser	buser	PROPN
ejpam-6985	185	8	’s	’s	PART
ejpam-6985	185	9	original	original	ADJ
ejpam-6985	185	10	strategy	strategy	NOUN
ejpam-6985	185	11	,	,	PUNCT
ejpam-6985	185	12	adapting	adapt	VERB
ejpam-6985	185	13	each	each	DET
ejpam-6985	185	14	step	step	NOUN
ejpam-6985	185	15	to	to	ADP
ejpam-6985	185	16	the	the	DET
ejpam-6985	185	17	cr	cr	PROPN
ejpam-6985	185	18	setting	set	VERB
ejpam-6985	185	19	.	.	PUNCT
ejpam-6985	186	1	step	step	NOUN
ejpam-6985	186	2	1	1	NUM
ejpam-6985	186	3	:	:	PUNCT
ejpam-6985	186	4	choice	choice	NOUN
ejpam-6985	186	5	of	of	ADP
ejpam-6985	186	6	an	an	DET
ejpam-6985	186	7	almost	almost	ADV
ejpam-6985	186	8	minimizer	minimizer	NOUN
ejpam-6985	186	9	.	.	PUNCT
ejpam-6985	187	1	by	by	ADP
ejpam-6985	187	2	definition	definition	NOUN
ejpam-6985	187	3	of	of	ADP
ejpam-6985	187	4	hcr(m	hcr(m	ADV
ejpam-6985	187	5	)	)	PUNCT
ejpam-6985	187	6	there	there	PRON
ejpam-6985	187	7	exists	exist	VERB
ejpam-6985	187	8	a	a	DET
ejpam-6985	187	9	measurable	measurable	ADJ
ejpam-6985	187	10	set	set	NOUN
ejpam-6985	187	11	e	e	SYM
ejpam-6985	187	12	⊂m	⊂m	PROPN
ejpam-6985	187	13	of	of	ADP
ejpam-6985	187	14	finite	finite	PROPN
ejpam-6985	187	15	horizontal	horizontal	PROPN
ejpam-6985	187	16	perimeter	perimeter	PROPN
ejpam-6985	187	17	such	such	ADJ
ejpam-6985	187	18	that	that	PRON
ejpam-6985	187	19	perh(e;m	perh(e;m	VERB
ejpam-6985	187	20	)	)	PUNCT
ejpam-6985	187	21	min{µ(e	min{µ(e	PROPN
ejpam-6985	187	22	)	)	PUNCT
ejpam-6985	187	23	,	,	PUNCT
ejpam-6985	187	24	µ(m	µ(m	PROPN
ejpam-6985	187	25	\	\	X
ejpam-6985	187	26	e	e	NOUN
ejpam-6985	187	27	)	)	PUNCT
ejpam-6985	187	28	}	}	PUNCT
ejpam-6985	187	29	≤	≤	NUM
ejpam-6985	187	30	2hcr(m	2hcr(m	NUM
ejpam-6985	187	31	)	)	PUNCT
ejpam-6985	187	32	.	.	PUNCT
ejpam-6985	188	1	(	(	PUNCT
ejpam-6985	188	2	4.3	4.3	NUM
ejpam-6985	188	3	)	)	PUNCT
ejpam-6985	188	4	we	we	PRON
ejpam-6985	188	5	may	may	AUX
ejpam-6985	188	6	assume	assume	VERB
ejpam-6985	188	7	µ(e	µ(e	PROPN
ejpam-6985	188	8	)	)	PUNCT
ejpam-6985	188	9	≤	≤	NUM
ejpam-6985	188	10	1	1	NUM
ejpam-6985	188	11	2µ(m	2µ(m	NUM
ejpam-6985	188	12	)	)	PUNCT
ejpam-6985	188	13	by	by	ADP
ejpam-6985	188	14	symmetry	symmetry	NOUN
ejpam-6985	188	15	.	.	PUNCT
ejpam-6985	189	1	by	by	ADP
ejpam-6985	189	2	standard	standard	ADJ
ejpam-6985	189	3	regularization	regularization	NOUN
ejpam-6985	189	4	arguments	argument	NOUN
ejpam-6985	189	5	(	(	PUNCT
ejpam-6985	189	6	see	see	VERB
ejpam-6985	189	7	[	[	X
ejpam-6985	189	8	6	6	NUM
ejpam-6985	189	9	]	]	NUM
ejpam-6985	189	10	)	)	PUNCT
ejpam-6985	189	11	,	,	PUNCT
ejpam-6985	189	12	e	e	NOUN
ejpam-6985	189	13	can	can	AUX
ejpam-6985	189	14	be	be	AUX
ejpam-6985	189	15	approximated	approximate	VERB
ejpam-6985	189	16	by	by	ADP
ejpam-6985	189	17	open	open	ADJ
ejpam-6985	189	18	sets	set	NOUN
ejpam-6985	189	19	with	with	ADP
ejpam-6985	189	20	smooth	smooth	ADJ
ejpam-6985	189	21	horizontal	horizontal	ADJ
ejpam-6985	189	22	boundary	boundary	NOUN
ejpam-6985	189	23	without	without	ADP
ejpam-6985	189	24	altering	alter	VERB
ejpam-6985	189	25	the	the	DET
ejpam-6985	189	26	ratio	ratio	NOUN
ejpam-6985	189	27	in	in	ADP
ejpam-6985	189	28	(	(	PUNCT
ejpam-6985	189	29	4.3	4.3	NUM
ejpam-6985	189	30	)	)	PUNCT
ejpam-6985	189	31	.	.	PUNCT
ejpam-6985	190	1	step	step	NOUN
ejpam-6985	190	2	2	2	NUM
ejpam-6985	190	3	:	:	PUNCT
ejpam-6985	190	4	cutoff	cutoff	NOUN
ejpam-6985	190	5	function	function	NOUN
ejpam-6985	190	6	construction	construction	NOUN
ejpam-6985	190	7	.	.	PUNCT
ejpam-6985	191	1	fix	fix	VERB
ejpam-6985	191	2	r	r	NOUN
ejpam-6985	191	3	>	>	X
ejpam-6985	191	4	0	0	PUNCT
ejpam-6985	191	5	small	small	ADJ
ejpam-6985	191	6	.	.	PUNCT
ejpam-6985	192	1	let	let	VERB
ejpam-6985	192	2	er	er	INTJ
ejpam-6985	192	3	=	=	X
ejpam-6985	192	4	{	{	PUNCT
ejpam-6985	192	5	x	x	SYM
ejpam-6985	192	6	∈	∈	NOUN
ejpam-6985	192	7	m	m	VERB
ejpam-6985	192	8	:	:	PUNCT
ejpam-6985	193	1	dcc(x	dcc(x	PROPN
ejpam-6985	193	2	,	,	PUNCT
ejpam-6985	193	3	e	e	NOUN
ejpam-6985	193	4	)	)	PUNCT
ejpam-6985	193	5	<	<	X
ejpam-6985	193	6	r	r	X
ejpam-6985	193	7	}	}	PUNCT
ejpam-6985	193	8	denote	denote	VERB
ejpam-6985	193	9	the	the	DET
ejpam-6985	193	10	carnot	carnot	NOUN
ejpam-6985	193	11	–	–	PUNCT
ejpam-6985	193	12	carathéodory	carathéodory	NOUN
ejpam-6985	193	13	r	r	NOUN
ejpam-6985	193	14	-	-	PUNCT
ejpam-6985	193	15	neighborhood	neighborhood	NOUN
ejpam-6985	193	16	.	.	PUNCT
ejpam-6985	194	1	choose	choose	VERB
ejpam-6985	194	2	a	a	DET
ejpam-6985	194	3	lipschitz	lipschitz	NOUN
ejpam-6985	194	4	cutoff	cutoff	ADP
ejpam-6985	194	5	ϕ	ϕ	PROPN
ejpam-6985	194	6	∈	∈	PROPN
ejpam-6985	194	7	lip(m	lip(m	PROPN
ejpam-6985	194	8	)	)	PUNCT
ejpam-6985	194	9	such	such	ADJ
ejpam-6985	194	10	that	that	SCONJ
ejpam-6985	194	11	ϕ	ϕ	PROPN
ejpam-6985	194	12	≡	≡	PROPN
ejpam-6985	194	13	1	1	NUM
ejpam-6985	194	14	on	on	ADP
ejpam-6985	194	15	e	e	NOUN
ejpam-6985	194	16	,	,	PUNCT
ejpam-6985	194	17	ϕ	ϕ	PROPN
ejpam-6985	194	18	≡	≡	PROPN
ejpam-6985	194	19	0	0	NUM
ejpam-6985	195	1	on	on	ADP
ejpam-6985	195	2	m	m	PROPN
ejpam-6985	195	3	\	\	PROPN
ejpam-6985	195	4	er	er	INTJ
ejpam-6985	195	5	,	,	PUNCT
ejpam-6985	195	6	|∇bϕ|	|∇bϕ|	PRON
ejpam-6985	195	7	≤	≤	NUM
ejpam-6985	195	8	c	c	NOUN
ejpam-6985	195	9	r	r	NOUN
ejpam-6985	195	10	a.e	a.e	PROPN
ejpam-6985	195	11	.	.	PROPN
ejpam-6985	195	12	,	,	PUNCT
ejpam-6985	195	13	where	where	SCONJ
ejpam-6985	195	14	,	,	PUNCT
ejpam-6985	195	15	c	c	PROPN
ejpam-6985	195	16	is	be	AUX
ejpam-6985	195	17	a	a	DET
ejpam-6985	195	18	universal	universal	ADJ
ejpam-6985	195	19	constant	constant	ADJ
ejpam-6985	195	20	depending	depend	VERB
ejpam-6985	195	21	only	only	ADV
ejpam-6985	195	22	on	on	ADP
ejpam-6985	195	23	the	the	DET
ejpam-6985	195	24	construction	construction	NOUN
ejpam-6985	195	25	.	.	PUNCT
ejpam-6985	196	1	such	such	DET
ejpam-6985	196	2	a	a	DET
ejpam-6985	196	3	function	function	NOUN
ejpam-6985	196	4	can	can	AUX
ejpam-6985	196	5	be	be	AUX
ejpam-6985	196	6	obtained	obtain	VERB
ejpam-6985	196	7	via	via	ADP
ejpam-6985	196	8	horizontal	horizontal	ADJ
ejpam-6985	196	9	mollification	mollification	NOUN
ejpam-6985	196	10	and	and	CCONJ
ejpam-6985	196	11	partition	partition	NOUN
ejpam-6985	196	12	of	of	ADP
ejpam-6985	196	13	unity	unity	NOUN
ejpam-6985	196	14	.	.	PUNCT
ejpam-6985	197	1	proposition	proposition	NOUN
ejpam-6985	197	2	6	6	NUM
ejpam-6985	197	3	(	(	PUNCT
ejpam-6985	197	4	rayleigh	rayleigh	PROPN
ejpam-6985	197	5	quotient	quotient	PROPN
ejpam-6985	197	6	estimate	estimate	PROPN
ejpam-6985	197	7	)	)	PUNCT
ejpam-6985	197	8	.	.	PUNCT
ejpam-6985	198	1	let	let	VERB
ejpam-6985	198	2	ϕ	ϕ	NOUN
ejpam-6985	198	3	be	be	AUX
ejpam-6985	198	4	as	as	ADV
ejpam-6985	198	5	above	above	ADV
ejpam-6985	198	6	.	.	PUNCT
ejpam-6985	199	1	then	then	ADV
ejpam-6985	199	2	r(ϕ	r(ϕ	PROPN
ejpam-6985	199	3	)	)	PUNCT
ejpam-6985	199	4	:	:	PUNCT
ejpam-6985	200	1	=	=	PUNCT
ejpam-6985	200	2	∫	∫	PROPN
ejpam-6985	200	3	m	m	PROPN
ejpam-6985	200	4	|∇bϕ|2	|∇bϕ|2	PROPN
ejpam-6985	200	5	dµ∫	dµ∫	PROPN
ejpam-6985	200	6	m	m	PROPN
ejpam-6985	200	7	(	(	PUNCT
ejpam-6985	200	8	ϕ−	ϕ−	PROPN
ejpam-6985	200	9	ϕ)2	ϕ)2	PROPN
ejpam-6985	200	10	dµ	dµ	VERB
ejpam-6985	200	11	≤	≤	ADJ
ejpam-6985	200	12	c3	c3	PROPN
ejpam-6985	200	13	r2	r2	PROPN
ejpam-6985	200	14	+	+	CCONJ
ejpam-6985	200	15	c4	c4	NOUN
ejpam-6985	200	16	r	r	NOUN
ejpam-6985	200	17	perh(e;m	perh(e;m	NOUN
ejpam-6985	200	18	)	)	PUNCT
ejpam-6985	200	19	µ(e	µ(e	PROPN
ejpam-6985	200	20	)	)	PUNCT
ejpam-6985	200	21	,	,	PUNCT
ejpam-6985	200	22	(	(	PUNCT
ejpam-6985	200	23	4.4	4.4	NUM
ejpam-6985	200	24	)	)	PUNCT
ejpam-6985	200	25	for	for	ADP
ejpam-6985	200	26	constants	constant	NOUN
ejpam-6985	200	27	c3	c3	PROPN
ejpam-6985	200	28	,	,	PUNCT
ejpam-6985	200	29	c4	c4	NOUN
ejpam-6985	200	30	depending	depend	VERB
ejpam-6985	200	31	only	only	ADV
ejpam-6985	200	32	on	on	ADP
ejpam-6985	200	33	the	the	DET
ejpam-6985	200	34	doubling	double	VERB
ejpam-6985	200	35	and	and	CCONJ
ejpam-6985	200	36	poincaré	poincaré	ADJ
ejpam-6985	200	37	data	datum	NOUN
ejpam-6985	200	38	.	.	PUNCT
ejpam-6985	201	1	proof	proof	NOUN
ejpam-6985	201	2	.	.	PUNCT
ejpam-6985	202	1	we	we	PRON
ejpam-6985	202	2	estimate	estimate	VERB
ejpam-6985	202	3	numerator	numerator	NOUN
ejpam-6985	202	4	and	and	CCONJ
ejpam-6985	202	5	denominator	denominator	NOUN
ejpam-6985	202	6	separately	separately	ADV
ejpam-6985	202	7	.	.	PUNCT
ejpam-6985	203	1	numerator	numerator	NOUN
ejpam-6985	203	2	.	.	PUNCT
ejpam-6985	204	1	by	by	ADP
ejpam-6985	204	2	the	the	DET
ejpam-6985	204	3	gradient	gradient	NOUN
ejpam-6985	204	4	bound	bind	VERB
ejpam-6985	204	5	|∇bϕ|	|∇bϕ|	PRON
ejpam-6985	204	6	≤	≤	NUM
ejpam-6985	204	7	c	c	NOUN
ejpam-6985	204	8	/	/	SYM
ejpam-6985	204	9	r	r	NOUN
ejpam-6985	204	10	and	and	CCONJ
ejpam-6985	204	11	support	support	NOUN
ejpam-6985	204	12	properties,∫	properties,∫	NOUN
ejpam-6985	204	13	m	m	VERB
ejpam-6985	204	14	|∇bϕ|2	|∇bϕ|2	NOUN
ejpam-6985	204	15	dµ	dµ	PROPN
ejpam-6985	204	16	≤	≤	PROPN
ejpam-6985	204	17	c2	c2	PROPN
ejpam-6985	204	18	r2	r2	PROPN
ejpam-6985	204	19	µ(er	µ(er	PART
ejpam-6985	204	20	\	\	PUNCT
ejpam-6985	204	21	e	e	X
ejpam-6985	204	22	)	)	PUNCT
ejpam-6985	204	23	.	.	PUNCT
ejpam-6985	205	1	by	by	ADP
ejpam-6985	205	2	the	the	DET
ejpam-6985	205	3	horizontal	horizontal	ADJ
ejpam-6985	205	4	co	co	NOUN
ejpam-6985	205	5	-	-	NOUN
ejpam-6985	205	6	area	area	NOUN
ejpam-6985	205	7	formula	formula	NOUN
ejpam-6985	205	8	(	(	PUNCT
ejpam-6985	205	9	proposition	proposition	NOUN
ejpam-6985	205	10	1	1	NUM
ejpam-6985	205	11	)	)	PUNCT
ejpam-6985	205	12	,	,	PUNCT
ejpam-6985	205	13	µ(er	µ(er	PROPN
ejpam-6985	205	14	\	\	PUNCT
ejpam-6985	205	15	e	e	X
ejpam-6985	205	16	)	)	PUNCT
ejpam-6985	205	17	≤	≤	PUNCT
ejpam-6985	205	18	c	c	NOUN
ejpam-6985	205	19	r	r	NOUN
ejpam-6985	205	20	perh(e;m	perh(e;m	NOUN
ejpam-6985	205	21	)	)	PUNCT
ejpam-6985	205	22	,	,	PUNCT
ejpam-6985	205	23	a.	a.	PROPN
ejpam-6985	205	24	ben	ben	PROPN
ejpam-6985	205	25	ahmed	ahmed	PROPN
ejpam-6985	205	26	/	/	SYM
ejpam-6985	205	27	eur	eur	PROPN
ejpam-6985	205	28	.	.	PUNCT
ejpam-6985	206	1	j.	j.	PROPN
ejpam-6985	206	2	pure	pure	PROPN
ejpam-6985	206	3	appl	appl	PROPN
ejpam-6985	206	4	.	.	PROPN
ejpam-6985	206	5	math	math	PROPN
ejpam-6985	206	6	,	,	PUNCT
ejpam-6985	206	7	18	18	NUM
ejpam-6985	206	8	(	(	PUNCT
ejpam-6985	206	9	4	4	NUM
ejpam-6985	206	10	)	)	PUNCT
ejpam-6985	206	11	(	(	PUNCT
ejpam-6985	206	12	2025	2025	NUM
ejpam-6985	206	13	)	)	PUNCT
ejpam-6985	206	14	,	,	PUNCT
ejpam-6985	206	15	6985	6985	NUM
ejpam-6985	206	16	10	10	NUM
ejpam-6985	206	17	of	of	ADP
ejpam-6985	206	18	16	16	NUM
ejpam-6985	206	19	for	for	ADP
ejpam-6985	206	20	a	a	DET
ejpam-6985	206	21	universal	universal	ADJ
ejpam-6985	206	22	constant	constant	ADJ
ejpam-6985	206	23	c	c	NOUN
ejpam-6985	206	24	depending	depend	VERB
ejpam-6985	206	25	only	only	ADV
ejpam-6985	206	26	on	on	ADP
ejpam-6985	206	27	doubling	double	VERB
ejpam-6985	206	28	.	.	PUNCT
ejpam-6985	207	1	hence∫	hence∫	PROPN
ejpam-6985	207	2	m	m	VERB
ejpam-6985	207	3	|∇bϕ|2	|∇bϕ|2	PROPN
ejpam-6985	207	4	dµ	dµ	VERB
ejpam-6985	207	5	≤	≤	NUM
ejpam-6985	208	1	c	c	NOUN
ejpam-6985	208	2	′	′	NUM
ejpam-6985	208	3	r	r	NOUN
ejpam-6985	208	4	perh(e;m	perh(e;m	NOUN
ejpam-6985	208	5	)	)	PUNCT
ejpam-6985	208	6	.	.	PUNCT
ejpam-6985	209	1	(	(	PUNCT
ejpam-6985	209	2	4.5	4.5	NUM
ejpam-6985	209	3	)	)	PUNCT
ejpam-6985	209	4	denominator	denominator	NOUN
ejpam-6985	209	5	.	.	PUNCT
ejpam-6985	210	1	since	since	SCONJ
ejpam-6985	210	2	ϕ	ϕ	NOUN
ejpam-6985	210	3	equals	equal	VERB
ejpam-6985	210	4	1	1	NUM
ejpam-6985	210	5	on	on	ADP
ejpam-6985	210	6	e	e	NOUN
ejpam-6985	210	7	and	and	CCONJ
ejpam-6985	210	8	vanishes	vanish	VERB
ejpam-6985	210	9	outside	outside	ADP
ejpam-6985	210	10	er	er	INTJ
ejpam-6985	210	11	,	,	PUNCT
ejpam-6985	210	12	its	its	PRON
ejpam-6985	210	13	average	average	ADJ
ejpam-6985	210	14	satisfies	satisfie	NOUN
ejpam-6985	210	15	ϕ	ϕ	NOUN
ejpam-6985	210	16	=	=	NOUN
ejpam-6985	210	17	1	1	NUM
ejpam-6985	210	18	µ(m	µ(m	NOUN
ejpam-6985	210	19	)	)	PUNCT
ejpam-6985	210	20	∫	∫	PROPN
ejpam-6985	210	21	m	m	PROPN
ejpam-6985	211	1	ϕ	ϕ	PROPN
ejpam-6985	211	2	dµ	dµ	PROPN
ejpam-6985	211	3	≤	≤	PROPN
ejpam-6985	211	4	µ(er	µ(er	ADV
ejpam-6985	211	5	)	)	PUNCT
ejpam-6985	212	1	µ(m	µ(m	NOUN
ejpam-6985	212	2	)	)	PUNCT
ejpam-6985	212	3	.	.	PUNCT
ejpam-6985	213	1	thus	thus	ADV
ejpam-6985	213	2	∫	∫	PROPN
ejpam-6985	213	3	m	m	PROPN
ejpam-6985	214	1	(	(	PUNCT
ejpam-6985	214	2	ϕ−	ϕ−	PROPN
ejpam-6985	214	3	ϕ)2	ϕ)2	PROPN
ejpam-6985	214	4	dµ	dµ	PROPN
ejpam-6985	214	5	≥	≥	PROPN
ejpam-6985	214	6	∫	∫	PROPN
ejpam-6985	214	7	e	e	X
ejpam-6985	214	8	(	(	PUNCT
ejpam-6985	214	9	1−	1−	NUM
ejpam-6985	214	10	ϕ)2	ϕ)2	PROPN
ejpam-6985	214	11	dµ	dµ	X
ejpam-6985	214	12	≥	≥	X
ejpam-6985	214	13	(	(	PUNCT
ejpam-6985	214	14	1−	1−	NUM
ejpam-6985	214	15	µ(er	µ(er	NUM
ejpam-6985	214	16	)	)	PUNCT
ejpam-6985	214	17	µ(m	µ(m	NOUN
ejpam-6985	214	18	)	)	PUNCT
ejpam-6985	214	19	)	)	PUNCT
ejpam-6985	214	20	2µ(e	2µ(e	NUM
ejpam-6985	214	21	)	)	PUNCT
ejpam-6985	214	22	.	.	PUNCT
ejpam-6985	215	1	by	by	ADP
ejpam-6985	215	2	doubling	double	VERB
ejpam-6985	215	3	,	,	PUNCT
ejpam-6985	215	4	µ(er	µ(er	ADV
ejpam-6985	215	5	)	)	PUNCT
ejpam-6985	215	6	≤	≤	NUM
ejpam-6985	215	7	c	c	X
ejpam-6985	215	8	µ(e	µ(e	PROPN
ejpam-6985	215	9	)	)	PUNCT
ejpam-6985	215	10	when	when	SCONJ
ejpam-6985	215	11	r	r	NOUN
ejpam-6985	215	12	is	be	AUX
ejpam-6985	215	13	chosen	choose	VERB
ejpam-6985	215	14	small	small	ADJ
ejpam-6985	215	15	compared	compare	VERB
ejpam-6985	215	16	to	to	ADP
ejpam-6985	215	17	diamcc(m	diamcc(m	PROPN
ejpam-6985	215	18	)	)	PUNCT
ejpam-6985	215	19	.	.	PUNCT
ejpam-6985	216	1	hence∫	hence∫	PROPN
ejpam-6985	216	2	m	m	VERB
ejpam-6985	216	3	(	(	PUNCT
ejpam-6985	216	4	ϕ−	ϕ−	PROPN
ejpam-6985	216	5	ϕ)2	ϕ)2	PROPN
ejpam-6985	216	6	dµ	dµ	PROPN
ejpam-6985	216	7	≥	≥	PROPN
ejpam-6985	216	8	c	c	PROPN
ejpam-6985	216	9	µ(e	µ(e	PROPN
ejpam-6985	216	10	)	)	PUNCT
ejpam-6985	216	11	,	,	PUNCT
ejpam-6985	216	12	(	(	PUNCT
ejpam-6985	216	13	4.6	4.6	NUM
ejpam-6985	216	14	)	)	PUNCT
ejpam-6985	216	15	for	for	ADP
ejpam-6985	216	16	some	some	DET
ejpam-6985	216	17	c	c	PROPN
ejpam-6985	216	18	>	>	X
ejpam-6985	216	19	0	0	PUNCT
ejpam-6985	217	1	depending	depend	VERB
ejpam-6985	217	2	only	only	ADV
ejpam-6985	217	3	on	on	ADP
ejpam-6985	217	4	doubling	double	VERB
ejpam-6985	217	5	.	.	PUNCT
ejpam-6985	218	1	rayleigh	rayleigh	PROPN
ejpam-6985	218	2	quotient	quotient	PROPN
ejpam-6985	218	3	.	.	PUNCT
ejpam-6985	219	1	combining	combine	VERB
ejpam-6985	219	2	(	(	PUNCT
ejpam-6985	219	3	4.5	4.5	NUM
ejpam-6985	219	4	)	)	PUNCT
ejpam-6985	219	5	and	and	CCONJ
ejpam-6985	219	6	(	(	PUNCT
ejpam-6985	219	7	4.6	4.6	NUM
ejpam-6985	219	8	)	)	PUNCT
ejpam-6985	219	9	yields	yield	NOUN
ejpam-6985	219	10	r(ϕ	r(ϕ	PROPN
ejpam-6985	219	11	)	)	PUNCT
ejpam-6985	219	12	≤	≤	PUNCT
ejpam-6985	220	1	c	c	X
ejpam-6985	221	1	′′	′′	PROPN
ejpam-6985	221	2	r	r	NOUN
ejpam-6985	221	3	perh(e;m	perh(e;m	PROPN
ejpam-6985	221	4	)	)	PUNCT
ejpam-6985	221	5	µ(e	µ(e	PROPN
ejpam-6985	221	6	)	)	PUNCT
ejpam-6985	221	7	.	.	PUNCT
ejpam-6985	222	1	finally	finally	ADV
ejpam-6985	222	2	,	,	PUNCT
ejpam-6985	222	3	an	an	DET
ejpam-6985	222	4	additional	additional	ADJ
ejpam-6985	222	5	term	term	NOUN
ejpam-6985	222	6	o(r−2	o(r−2	NOUN
ejpam-6985	222	7	)	)	PUNCT
ejpam-6985	222	8	arises	arise	VERB
ejpam-6985	222	9	from	from	ADP
ejpam-6985	222	10	the	the	DET
ejpam-6985	222	11	contribution	contribution	NOUN
ejpam-6985	222	12	of	of	ADP
ejpam-6985	222	13	µ(er	µ(er	NOUN
ejpam-6985	222	14	\	\	NOUN
ejpam-6985	222	15	e	e	X
ejpam-6985	222	16	)	)	PUNCT
ejpam-6985	222	17	when	when	SCONJ
ejpam-6985	222	18	e	e	NOUN
ejpam-6985	222	19	is	be	AUX
ejpam-6985	222	20	small	small	ADJ
ejpam-6985	222	21	compared	compare	VERB
ejpam-6985	222	22	to	to	ADP
ejpam-6985	222	23	m	m	PRON
ejpam-6985	222	24	,	,	PUNCT
ejpam-6985	222	25	leading	lead	VERB
ejpam-6985	222	26	to	to	ADP
ejpam-6985	222	27	the	the	DET
ejpam-6985	222	28	full	full	ADJ
ejpam-6985	222	29	bound	bind	VERB
ejpam-6985	222	30	(	(	PUNCT
ejpam-6985	222	31	4.4	4.4	NUM
ejpam-6985	222	32	)	)	PUNCT
ejpam-6985	222	33	.	.	PUNCT
ejpam-6985	223	1	step	step	NOUN
ejpam-6985	223	2	3	3	NUM
ejpam-6985	223	3	:	:	PUNCT
ejpam-6985	223	4	optimization	optimization	NOUN
ejpam-6985	223	5	.	.	PUNCT
ejpam-6985	224	1	by	by	ADP
ejpam-6985	224	2	(	(	PUNCT
ejpam-6985	224	3	4.3	4.3	NUM
ejpam-6985	224	4	)	)	PUNCT
ejpam-6985	224	5	,	,	PUNCT
ejpam-6985	224	6	perh(e;m)/µ(e	perh(e;m)/µ(e	X
ejpam-6985	224	7	)	)	PUNCT
ejpam-6985	224	8	≤	≤	NOUN
ejpam-6985	224	9	2hcr(m	2hcr(m	NUM
ejpam-6985	224	10	)	)	PUNCT
ejpam-6985	224	11	.	.	PUNCT
ejpam-6985	225	1	proposition	proposition	NOUN
ejpam-6985	225	2	6	6	NUM
ejpam-6985	225	3	gives	give	VERB
ejpam-6985	225	4	r(ϕ	r(ϕ	PROPN
ejpam-6985	225	5	)	)	PUNCT
ejpam-6985	225	6	≤	≤	NOUN
ejpam-6985	225	7	c3	c3	NOUN
ejpam-6985	225	8	r2	r2	PROPN
ejpam-6985	226	1	+	+	CCONJ
ejpam-6985	226	2	2c4	2c4	NUM
ejpam-6985	226	3	r	r	NOUN
ejpam-6985	226	4	hcr(m	hcr(m	NOUN
ejpam-6985	226	5	)	)	PUNCT
ejpam-6985	226	6	.	.	PUNCT
ejpam-6985	227	1	optimizing	optimize	VERB
ejpam-6985	227	2	in	in	ADP
ejpam-6985	227	3	r	r	NOUN
ejpam-6985	227	4	by	by	ADP
ejpam-6985	227	5	taking	take	VERB
ejpam-6985	227	6	r	r	NOUN
ejpam-6985	227	7	∼	∼	NOUN
ejpam-6985	227	8	1	1	NUM
ejpam-6985	227	9	/	/	SYM
ejpam-6985	227	10	hcr(m	hcr(m	NOUN
ejpam-6985	227	11	)	)	PUNCT
ejpam-6985	227	12	yields	yield	NOUN
ejpam-6985	227	13	r(ϕ	r(ϕ	PROPN
ejpam-6985	227	14	)	)	PUNCT
ejpam-6985	227	15	≤	≤	PROPN
ejpam-6985	227	16	c1	c1	PROPN
ejpam-6985	227	17	hcr(m)2	hcr(m)2	VERB
ejpam-6985	227	18	+	+	CCONJ
ejpam-6985	227	19	c2	c2	PROPN
ejpam-6985	227	20	hcr(m	hcr(m	PROPN
ejpam-6985	227	21	)	)	PUNCT
ejpam-6985	227	22	.	.	PUNCT
ejpam-6985	228	1	step	step	NOUN
ejpam-6985	228	2	4	4	NUM
ejpam-6985	228	3	:	:	PUNCT
ejpam-6985	228	4	variational	variational	ADJ
ejpam-6985	228	5	principle	principle	NOUN
ejpam-6985	228	6	.	.	PUNCT
ejpam-6985	229	1	since	since	SCONJ
ejpam-6985	229	2	ϕ	ϕ	PROPN
ejpam-6985	229	3	is	be	AUX
ejpam-6985	229	4	non	non	ADJ
ejpam-6985	229	5	-	-	ADJ
ejpam-6985	229	6	constant	constant	ADJ
ejpam-6985	229	7	,	,	PUNCT
ejpam-6985	229	8	the	the	DET
ejpam-6985	229	9	rayleigh	rayleigh	PROPN
ejpam-6985	229	10	quotient	quotient	NOUN
ejpam-6985	229	11	r(ϕ	r(ϕ	PROPN
ejpam-6985	229	12	)	)	PUNCT
ejpam-6985	229	13	bounds	bound	VERB
ejpam-6985	229	14	λ1(∆b	λ1(∆b	NOUN
ejpam-6985	229	15	)	)	PUNCT
ejpam-6985	229	16	from	from	ADP
ejpam-6985	229	17	above	above	ADV
ejpam-6985	229	18	:	:	PUNCT
ejpam-6985	229	19	λ1(∆b	λ1(∆b	NOUN
ejpam-6985	229	20	)	)	PUNCT
ejpam-6985	229	21	≤	≤	NOUN
ejpam-6985	229	22	r(ϕ	r(ϕ	PROPN
ejpam-6985	229	23	)	)	PUNCT
ejpam-6985	229	24	.	.	PUNCT
ejpam-6985	230	1	this	this	PRON
ejpam-6985	230	2	proves	prove	VERB
ejpam-6985	230	3	theorem	theorem	ADJ
ejpam-6985	230	4	2	2	NUM
ejpam-6985	230	5	.	.	PUNCT
ejpam-6985	230	6	.	.	PUNCT
ejpam-6985	231	1	remark	remark	PROPN
ejpam-6985	231	2	3	3	NUM
ejpam-6985	231	3	.	.	PUNCT
ejpam-6985	232	1	the	the	DET
ejpam-6985	232	2	theorem	theorem	NOUN
ejpam-6985	232	3	is	be	AUX
ejpam-6985	232	4	conditional	conditional	ADJ
ejpam-6985	232	5	on	on	ADP
ejpam-6985	232	6	assumptions	assumption	NOUN
ejpam-6985	232	7	(	(	PUNCT
ejpam-6985	232	8	a1)–(a2	a1)–(a2	NOUN
ejpam-6985	232	9	)	)	PUNCT
ejpam-6985	232	10	.	.	PUNCT
ejpam-6985	233	1	these	these	DET
ejpam-6985	233	2	conditions	condition	NOUN
ejpam-6985	233	3	are	be	AUX
ejpam-6985	233	4	satisfied	satisfied	ADJ
ejpam-6985	233	5	in	in	ADP
ejpam-6985	233	6	many	many	ADJ
ejpam-6985	233	7	natural	natural	ADJ
ejpam-6985	233	8	examples	example	NOUN
ejpam-6985	233	9	,	,	PUNCT
ejpam-6985	233	10	such	such	ADJ
ejpam-6985	233	11	as	as	ADP
ejpam-6985	233	12	compact	compact	ADJ
ejpam-6985	233	13	quotients	quotient	NOUN
ejpam-6985	233	14	of	of	ADP
ejpam-6985	233	15	heisenberg	heisenberg	PROPN
ejpam-6985	233	16	-	-	PUNCT
ejpam-6985	233	17	type	type	NOUN
ejpam-6985	233	18	groups	group	NOUN
ejpam-6985	233	19	and	and	CCONJ
ejpam-6985	233	20	compact	compact	ADJ
ejpam-6985	233	21	sasakian	sasakian	NOUN
ejpam-6985	233	22	manifolds	manifold	NOUN
ejpam-6985	233	23	with	with	ADP
ejpam-6985	233	24	uniformly	uniformly	ADV
ejpam-6985	233	25	bounded	bound	VERB
ejpam-6985	233	26	webster	webster	PROPN
ejpam-6985	233	27	curvature	curvature	PROPN
ejpam-6985	233	28	and	and	CCONJ
ejpam-6985	233	29	torsion	torsion	NOUN
ejpam-6985	233	30	.	.	PUNCT
ejpam-6985	234	1	the	the	DET
ejpam-6985	234	2	dependence	dependence	NOUN
ejpam-6985	234	3	on	on	ADP
ejpam-6985	234	4	torsion	torsion	NOUN
ejpam-6985	234	5	is	be	AUX
ejpam-6985	234	6	only	only	ADV
ejpam-6985	234	7	through	through	ADP
ejpam-6985	234	8	the	the	DET
ejpam-6985	234	9	analytic	analytic	ADJ
ejpam-6985	234	10	constants	constant	NOUN
ejpam-6985	234	11	controlling	control	VERB
ejpam-6985	234	12	the	the	DET
ejpam-6985	234	13	doubling	double	VERB
ejpam-6985	234	14	and	and	CCONJ
ejpam-6985	234	15	poincaré	poincaré	ADJ
ejpam-6985	234	16	properties	property	NOUN
ejpam-6985	234	17	,	,	PUNCT
ejpam-6985	234	18	rather	rather	ADV
ejpam-6985	234	19	than	than	ADP
ejpam-6985	234	20	explicitly	explicitly	ADV
ejpam-6985	234	21	in	in	ADP
ejpam-6985	234	22	the	the	DET
ejpam-6985	234	23	inequality	inequality	NOUN
ejpam-6985	234	24	(	(	PUNCT
ejpam-6985	234	25	4.2	4.2	NUM
ejpam-6985	234	26	)	)	PUNCT
ejpam-6985	234	27	.	.	PUNCT
ejpam-6985	235	1	a.	a.	PROPN
ejpam-6985	235	2	ben	ben	PROPN
ejpam-6985	235	3	ahmed	ahmed	PROPN
ejpam-6985	235	4	/	/	SYM
ejpam-6985	235	5	eur	eur	PROPN
ejpam-6985	235	6	.	.	PUNCT
ejpam-6985	236	1	j.	j.	PROPN
ejpam-6985	236	2	pure	pure	PROPN
ejpam-6985	236	3	appl	appl	PROPN
ejpam-6985	236	4	.	.	PROPN
ejpam-6985	236	5	math	math	PROPN
ejpam-6985	236	6	,	,	PUNCT
ejpam-6985	236	7	18	18	NUM
ejpam-6985	236	8	(	(	PUNCT
ejpam-6985	236	9	4	4	NUM
ejpam-6985	236	10	)	)	PUNCT
ejpam-6985	236	11	(	(	PUNCT
ejpam-6985	236	12	2025	2025	NUM
ejpam-6985	236	13	)	)	PUNCT
ejpam-6985	236	14	,	,	PUNCT
ejpam-6985	236	15	6985	6985	NUM
ejpam-6985	236	16	11	11	NUM
ejpam-6985	236	17	of	of	ADP
ejpam-6985	236	18	16	16	NUM
ejpam-6985	236	19	5	5	NUM
ejpam-6985	236	20	.	.	PUNCT
ejpam-6985	236	21	model	model	NOUN
ejpam-6985	236	22	computations	computation	NOUN
ejpam-6985	236	23	and	and	CCONJ
ejpam-6985	236	24	examples	example	NOUN
ejpam-6985	236	25	5.1	5.1	NUM
ejpam-6985	236	26	.	.	PUNCT
ejpam-6985	237	1	compact	compact	ADJ
ejpam-6985	237	2	quotients	quotient	NOUN
ejpam-6985	237	3	of	of	ADP
ejpam-6985	237	4	the	the	DET
ejpam-6985	237	5	heisenberg	heisenberg	PROPN
ejpam-6985	237	6	group	group	PROPN
ejpam-6985	237	7	let	let	VERB
ejpam-6985	237	8	hn	hn	PRON
ejpam-6985	237	9	denote	denote	VERB
ejpam-6985	237	10	the	the	DET
ejpam-6985	237	11	(	(	PUNCT
ejpam-6985	237	12	2n+1)-dimensional	2n+1)-dimensional	PROPN
ejpam-6985	237	13	heisenberg	heisenberg	PROPN
ejpam-6985	237	14	group	group	NOUN
ejpam-6985	237	15	with	with	ADP
ejpam-6985	237	16	its	its	PRON
ejpam-6985	237	17	standard	standard	ADJ
ejpam-6985	237	18	left	left	ADJ
ejpam-6985	237	19	-	-	PUNCT
ejpam-6985	237	20	invariant	invariant	ADJ
ejpam-6985	237	21	contact	contact	NOUN
ejpam-6985	237	22	form	form	NOUN
ejpam-6985	237	23	and	and	CCONJ
ejpam-6985	237	24	horizontal	horizontal	ADJ
ejpam-6985	237	25	distribution	distribution	NOUN
ejpam-6985	237	26	.	.	PUNCT
ejpam-6985	238	1	for	for	ADP
ejpam-6985	238	2	a	a	DET
ejpam-6985	238	3	compact	compact	ADJ
ejpam-6985	238	4	quotient	quotient	NOUN
ejpam-6985	238	5	m	m	NOUN
ejpam-6985	238	6	=	=	SYM
ejpam-6985	238	7	γ\hn	γ\hn	PROPN
ejpam-6985	238	8	(	(	PUNCT
ejpam-6985	238	9	with	with	ADP
ejpam-6985	238	10	haar	haar	PROPN
ejpam-6985	238	11	measure	measure	NOUN
ejpam-6985	238	12	)	)	PUNCT
ejpam-6985	238	13	,	,	PUNCT
ejpam-6985	238	14	the	the	DET
ejpam-6985	238	15	horizontal	horizontal	ADJ
ejpam-6985	238	16	structure	structure	NOUN
ejpam-6985	238	17	is	be	AUX
ejpam-6985	238	18	homogeneous	homogeneous	ADJ
ejpam-6985	238	19	and	and	CCONJ
ejpam-6985	238	20	torsion	torsion	NOUN
ejpam-6985	238	21	-	-	PUNCT
ejpam-6985	238	22	free	free	ADJ
ejpam-6985	238	23	;	;	PUNCT
ejpam-6985	238	24	classical	classical	ADJ
ejpam-6985	238	25	isoperimetric	isoperimetric	NOUN
ejpam-6985	238	26	and	and	CCONJ
ejpam-6985	238	27	sobolev	sobolev	NOUN
ejpam-6985	238	28	inequalities	inequality	NOUN
ejpam-6985	238	29	are	be	AUX
ejpam-6985	238	30	sharp	sharp	ADJ
ejpam-6985	238	31	in	in	ADP
ejpam-6985	238	32	this	this	DET
ejpam-6985	238	33	case	case	NOUN
ejpam-6985	238	34	[	[	X
ejpam-6985	238	35	3	3	NUM
ejpam-6985	238	36	,	,	PUNCT
ejpam-6985	238	37	9	9	NUM
ejpam-6985	238	38	]	]	PUNCT
ejpam-6985	238	39	.	.	PUNCT
ejpam-6985	239	1	hence	hence	ADV
ejpam-6985	239	2	the	the	DET
ejpam-6985	239	3	cheeger	cheeger	ADJ
ejpam-6985	239	4	–	–	PUNCT
ejpam-6985	239	5	cr	cr	PROPN
ejpam-6985	239	6	inequality	inequality	NOUN
ejpam-6985	239	7	holds	hold	VERB
ejpam-6985	239	8	with	with	ADP
ejpam-6985	239	9	c∗	c∗	NOUN
ejpam-6985	239	10	=	=	SYM
ejpam-6985	239	11	1	1	NUM
ejpam-6985	239	12	4	4	NUM
ejpam-6985	239	13	under	under	ADP
ejpam-6985	239	14	the	the	DET
ejpam-6985	239	15	standard	standard	ADJ
ejpam-6985	239	16	normalization	normalization	NOUN
ejpam-6985	239	17	of	of	ADP
ejpam-6985	239	18	∆b	∆b	PROPN
ejpam-6985	239	19	on	on	ADP
ejpam-6985	239	20	m	m	PROPN
ejpam-6985	239	21	.	.	PUNCT
ejpam-6985	240	1	5.2	5.2	NUM
ejpam-6985	240	2	.	.	PUNCT
ejpam-6985	241	1	the	the	DET
ejpam-6985	241	2	standard	standard	PROPN
ejpam-6985	241	3	cr	cr	PRON
ejpam-6985	241	4	sphere	sphere	ADV
ejpam-6985	241	5	s2n+1	s2n+1	ADP
ejpam-6985	241	6	the	the	DET
ejpam-6985	241	7	standard	standard	NOUN
ejpam-6985	241	8	cr	cr	PRON
ejpam-6985	241	9	sphere	sphere	ADV
ejpam-6985	241	10	s2n+1	s2n+1	PROPN
ejpam-6985	241	11	⊂	⊂	X
ejpam-6985	241	12	cn+1	cn+1	VERB
ejpam-6985	241	13	with	with	ADP
ejpam-6985	241	14	contact	contact	NOUN
ejpam-6985	241	15	form	form	NOUN
ejpam-6985	241	16	induced	induce	VERB
ejpam-6985	241	17	by	by	ADP
ejpam-6985	241	18	the	the	DET
ejpam-6985	241	19	euclidean	euclidean	ADJ
ejpam-6985	241	20	form	form	NOUN
ejpam-6985	241	21	is	be	AUX
ejpam-6985	241	22	the	the	DET
ejpam-6985	241	23	canonical	canonical	ADJ
ejpam-6985	241	24	compact	compact	ADJ
ejpam-6985	241	25	model	model	NOUN
ejpam-6985	241	26	.	.	PUNCT
ejpam-6985	242	1	important	important	ADJ
ejpam-6985	242	2	spectral	spectral	ADJ
ejpam-6985	242	3	facts	fact	NOUN
ejpam-6985	242	4	(	(	PUNCT
ejpam-6985	242	5	folland	folland	NOUN
ejpam-6985	242	6	–	–	PUNCT
ejpam-6985	242	7	stein	stein	NOUN
ejpam-6985	243	1	[	[	X
ejpam-6985	243	2	3	3	NUM
ejpam-6985	243	3	]	]	PUNCT
ejpam-6985	243	4	)	)	PUNCT
ejpam-6985	243	5	indicate	indicate	VERB
ejpam-6985	243	6	that	that	SCONJ
ejpam-6985	243	7	eigenvalues	eigenvalue	NOUN
ejpam-6985	243	8	of	of	ADP
ejpam-6985	243	9	the	the	DET
ejpam-6985	243	10	sub	sub	ADJ
ejpam-6985	243	11	-	-	ADJ
ejpam-6985	243	12	laplacian	laplacian	ADJ
ejpam-6985	243	13	acting	acting	NOUN
ejpam-6985	243	14	on	on	ADP
ejpam-6985	243	15	functions	function	NOUN
ejpam-6985	243	16	arise	arise	VERB
ejpam-6985	243	17	from	from	ADP
ejpam-6985	243	18	spherical	spherical	ADJ
ejpam-6985	243	19	harmonics	harmonic	NOUN
ejpam-6985	243	20	and	and	CCONJ
ejpam-6985	243	21	with	with	ADP
ejpam-6985	243	22	a	a	DET
ejpam-6985	243	23	convenient	convenient	ADJ
ejpam-6985	243	24	normalization	normalization	NOUN
ejpam-6985	243	25	,	,	PUNCT
ejpam-6985	243	26	are	be	AUX
ejpam-6985	243	27	of	of	ADP
ejpam-6985	243	28	the	the	DET
ejpam-6985	243	29	form	form	NOUN
ejpam-6985	244	1	λk	λk	X
ejpam-6985	244	2	=	=	PUNCT
ejpam-6985	244	3	k(k	k(k	PROPN
ejpam-6985	244	4	+	+	NUM
ejpam-6985	244	5	2n	2n	NUM
ejpam-6985	244	6	)	)	PUNCT
ejpam-6985	244	7	,	,	PUNCT
ejpam-6985	244	8	k	k	PROPN
ejpam-6985	244	9	∈	∈	PROPN
ejpam-6985	244	10	n.	n.	NOUN
ejpam-6985	244	11	thus	thus	ADV
ejpam-6985	244	12	the	the	DET
ejpam-6985	244	13	first	first	ADJ
ejpam-6985	244	14	positive	positive	ADJ
ejpam-6985	244	15	eigenvalue	eigenvalue	NOUN
ejpam-6985	244	16	corresponds	correspond	NOUN
ejpam-6985	244	17	to	to	ADP
ejpam-6985	244	18	k	k	PROPN
ejpam-6985	244	19	=	=	SYM
ejpam-6985	244	20	1	1	NUM
ejpam-6985	244	21	,	,	PUNCT
ejpam-6985	244	22	giving	give	VERB
ejpam-6985	244	23	λ1	λ1	ADJ
ejpam-6985	244	24	=	=	SYM
ejpam-6985	244	25	2n	2n	NUM
ejpam-6985	245	1	+	+	CCONJ
ejpam-6985	245	2	1	1	X
ejpam-6985	245	3	.	.	X
ejpam-6985	245	4	(	(	PUNCT
ejpam-6985	245	5	different	different	ADJ
ejpam-6985	245	6	normalizations	normalization	NOUN
ejpam-6985	245	7	of	of	ADP
ejpam-6985	245	8	θ	θ	PROPN
ejpam-6985	245	9	or	or	CCONJ
ejpam-6985	245	10	∆b	∆b	PROPN
ejpam-6985	245	11	shift	shift	VERB
ejpam-6985	245	12	these	these	DET
ejpam-6985	245	13	numbers	number	NOUN
ejpam-6985	245	14	;	;	PUNCT
ejpam-6985	245	15	the	the	DET
ejpam-6985	245	16	stated	state	VERB
ejpam-6985	245	17	relation	relation	NOUN
ejpam-6985	245	18	matches	match	VERB
ejpam-6985	245	19	the	the	DET
ejpam-6985	245	20	standard	standard	ADJ
ejpam-6985	245	21	choice	choice	NOUN
ejpam-6985	245	22	in	in	ADP
ejpam-6985	245	23	[	[	X
ejpam-6985	245	24	3	3	NUM
ejpam-6985	245	25	]	]	PUNCT
ejpam-6985	245	26	.	.	PUNCT
ejpam-6985	245	27	)	)	PUNCT
ejpam-6985	246	1	by	by	ADP
ejpam-6985	246	2	symmetry	symmetry	NOUN
ejpam-6985	246	3	,	,	PUNCT
ejpam-6985	246	4	isoperimetric	isoperimetric	ADJ
ejpam-6985	246	5	minimizers	minimizer	NOUN
ejpam-6985	246	6	are	be	AUX
ejpam-6985	246	7	spherical	spherical	ADJ
ejpam-6985	246	8	caps	cap	NOUN
ejpam-6985	246	9	;	;	PUNCT
ejpam-6985	246	10	hence	hence	ADV
ejpam-6985	246	11	hcr(s	hcr(s	PROPN
ejpam-6985	246	12	2n+1	2n+1	PROPN
ejpam-6985	246	13	)	)	PUNCT
ejpam-6985	246	14	is	be	AUX
ejpam-6985	246	15	a	a	DET
ejpam-6985	246	16	positive	positive	ADJ
ejpam-6985	246	17	constant	constant	ADJ
ejpam-6985	246	18	depending	depend	VERB
ejpam-6985	246	19	only	only	ADV
ejpam-6985	246	20	on	on	ADP
ejpam-6985	246	21	n	n	PRON
ejpam-6985	246	22	and	and	CCONJ
ejpam-6985	246	23	the	the	DET
ejpam-6985	246	24	cheeger	cheeger	ADJ
ejpam-6985	246	25	–	–	PUNCT
ejpam-6985	246	26	cr	cr	NOUN
ejpam-6985	246	27	lower	lower	ADV
ejpam-6985	246	28	bound	bind	VERB
ejpam-6985	246	29	is	be	AUX
ejpam-6985	246	30	consistent	consistent	ADJ
ejpam-6985	246	31	with	with	ADP
ejpam-6985	246	32	these	these	DET
ejpam-6985	246	33	values	value	NOUN
ejpam-6985	246	34	.	.	PUNCT
ejpam-6985	247	1	6	6	X
ejpam-6985	247	2	.	.	X
ejpam-6985	247	3	rossi	rossi	PROPN
ejpam-6985	247	4	’s	’s	PART
ejpam-6985	247	5	spheres	sphere	NOUN
ejpam-6985	247	6	and	and	CCONJ
ejpam-6985	247	7	spectral	spectral	ADJ
ejpam-6985	247	8	perturbation	perturbation	NOUN
ejpam-6985	247	9	6.1	6.1	NUM
ejpam-6985	247	10	.	.	PUNCT
ejpam-6985	248	1	historical	historical	ADJ
ejpam-6985	248	2	and	and	CCONJ
ejpam-6985	248	3	mathematical	mathematical	ADJ
ejpam-6985	248	4	context	context	NOUN
ejpam-6985	248	5	in	in	ADP
ejpam-6985	248	6	1965	1965	NUM
ejpam-6985	248	7	rossi	rossi	NOUN
ejpam-6985	249	1	[	[	X
ejpam-6985	249	2	14	14	NUM
ejpam-6985	249	3	]	]	PUNCT
ejpam-6985	249	4	produced	produce	VERB
ejpam-6985	249	5	one	one	NUM
ejpam-6985	249	6	of	of	ADP
ejpam-6985	249	7	the	the	DET
ejpam-6985	249	8	first	first	ADJ
ejpam-6985	249	9	explicit	explicit	ADJ
ejpam-6985	249	10	examples	example	NOUN
ejpam-6985	249	11	of	of	ADP
ejpam-6985	249	12	compact	compact	ADJ
ejpam-6985	249	13	strictly	strictly	ADV
ejpam-6985	249	14	pseudoconvex	pseudoconvex	PROPN
ejpam-6985	249	15	cr	cr	PROPN
ejpam-6985	249	16	manifolds	manifold	NOUN
ejpam-6985	249	17	that	that	PRON
ejpam-6985	249	18	are	be	AUX
ejpam-6985	249	19	not	not	PART
ejpam-6985	249	20	globally	globally	ADV
ejpam-6985	249	21	embeddable	embeddable	ADJ
ejpam-6985	249	22	as	as	ADP
ejpam-6985	249	23	hypersurfaces	hypersurface	NOUN
ejpam-6985	249	24	in	in	ADP
ejpam-6985	249	25	any	any	DET
ejpam-6985	249	26	cn	cn	PROPN
ejpam-6985	249	27	.	.	PUNCT
ejpam-6985	250	1	rossi	rossi	PROPN
ejpam-6985	250	2	’s	’s	PART
ejpam-6985	250	3	construction	construction	NOUN
ejpam-6985	250	4	demonstrated	demonstrate	VERB
ejpam-6985	250	5	that	that	SCONJ
ejpam-6985	250	6	integrability	integrability	NOUN
ejpam-6985	250	7	and	and	CCONJ
ejpam-6985	250	8	embeddability	embeddability	NOUN
ejpam-6985	250	9	in	in	ADP
ejpam-6985	250	10	cr	cr	NOUN
ejpam-6985	250	11	geometry	geometry	NOUN
ejpam-6985	250	12	are	be	AUX
ejpam-6985	250	13	subtler	subtle	ADJ
ejpam-6985	250	14	than	than	ADP
ejpam-6985	250	15	in	in	ADP
ejpam-6985	250	16	the	the	DET
ejpam-6985	250	17	almost	almost	ADV
ejpam-6985	250	18	-	-	PUNCT
ejpam-6985	250	19	complex	complex	ADJ
ejpam-6985	250	20	case	case	NOUN
ejpam-6985	250	21	and	and	CCONJ
ejpam-6985	250	22	triggered	trigger	VERB
ejpam-6985	250	23	many	many	ADJ
ejpam-6985	250	24	subsequent	subsequent	ADJ
ejpam-6985	250	25	works	work	NOUN
ejpam-6985	250	26	(	(	PUNCT
ejpam-6985	250	27	kohn	kohn	PROPN
ejpam-6985	250	28	,	,	PUNCT
ejpam-6985	250	29	nirenberg	nirenberg	PROPN
ejpam-6985	250	30	,	,	PUNCT
ejpam-6985	250	31	burns	burn	NOUN
ejpam-6985	250	32	–	–	PUNCT
ejpam-6985	250	33	epstein	epstein	PROPN
ejpam-6985	250	34	,	,	PUNCT
ejpam-6985	250	35	huang	huang	PROPN
ejpam-6985	250	36	–	–	PUNCT
ejpam-6985	250	37	siu	siu	NOUN
ejpam-6985	250	38	and	and	CCONJ
ejpam-6985	250	39	others	other	NOUN
ejpam-6985	250	40	)	)	PUNCT
ejpam-6985	250	41	.	.	PUNCT
ejpam-6985	251	1	rossi	rossi	PROPN
ejpam-6985	251	2	’s	’s	PART
ejpam-6985	251	3	deformations	deformation	NOUN
ejpam-6985	251	4	are	be	AUX
ejpam-6985	251	5	defined	define	VERB
ejpam-6985	251	6	on	on	ADP
ejpam-6985	251	7	the	the	DET
ejpam-6985	251	8	underlying	underlying	ADJ
ejpam-6985	251	9	c∞	c∞	PROPN
ejpam-6985	251	10	manifold	manifold	ADJ
ejpam-6985	251	11	s3	s3	PROPN
ejpam-6985	251	12	and	and	CCONJ
ejpam-6985	251	13	yield	yield	VERB
ejpam-6985	251	14	inequivalent	inequivalent	NOUN
ejpam-6985	251	15	cr	cr	PROPN
ejpam-6985	251	16	structures	structure	NOUN
ejpam-6985	251	17	with	with	ADP
ejpam-6985	251	18	different	different	ADJ
ejpam-6985	251	19	analytic	analytic	ADJ
ejpam-6985	251	20	properties	property	NOUN
ejpam-6985	251	21	.	.	PUNCT
ejpam-6985	252	1	6.2	6.2	NUM
ejpam-6985	252	2	.	.	PUNCT
ejpam-6985	253	1	an	an	DET
ejpam-6985	253	2	explicit	explicit	ADJ
ejpam-6985	253	3	local	local	ADJ
ejpam-6985	253	4	deformation	deformation	NOUN
ejpam-6985	253	5	we	we	PRON
ejpam-6985	253	6	present	present	VERB
ejpam-6985	253	7	a	a	DET
ejpam-6985	253	8	local	local	ADJ
ejpam-6985	253	9	description	description	NOUN
ejpam-6985	253	10	of	of	ADP
ejpam-6985	253	11	a	a	DET
ejpam-6985	253	12	family	family	NOUN
ejpam-6985	253	13	of	of	ADP
ejpam-6985	253	14	deformations	deformation	NOUN
ejpam-6985	253	15	which	which	PRON
ejpam-6985	253	16	will	will	AUX
ejpam-6985	253	17	be	be	AUX
ejpam-6985	253	18	useful	useful	ADJ
ejpam-6985	253	19	for	for	ADP
ejpam-6985	253	20	discussing	discuss	VERB
ejpam-6985	253	21	spectral	spectral	ADJ
ejpam-6985	253	22	perturbation	perturbation	NOUN
ejpam-6985	253	23	.	.	PUNCT
ejpam-6985	254	1	let	let	VERB
ejpam-6985	254	2	s3	s3	PROPN
ejpam-6985	254	3	⊂	⊂	PROPN
ejpam-6985	254	4	c2	c2	PROPN
ejpam-6985	254	5	with	with	ADP
ejpam-6985	254	6	coordinates	coordinate	NOUN
ejpam-6985	254	7	(	(	PUNCT
ejpam-6985	254	8	z1	z1	PROPN
ejpam-6985	254	9	,	,	PUNCT
ejpam-6985	254	10	z2	z2	PROPN
ejpam-6985	254	11	)	)	PUNCT
ejpam-6985	254	12	and	and	CCONJ
ejpam-6985	254	13	let	let	VERB
ejpam-6985	254	14	l	l	NOUN
ejpam-6985	254	15	=	=	SYM
ejpam-6985	254	16	z2	z2	PROPN
ejpam-6985	254	17	∂	∂	NUM
ejpam-6985	254	18	∂z1	∂z1	PROPN
ejpam-6985	254	19	−	−	PROPN
ejpam-6985	254	20	z1	z1	PROPN
ejpam-6985	254	21	∂	∂	NUM
ejpam-6985	254	22	∂z2	∂z2	NOUN
ejpam-6985	254	23	(	(	PUNCT
ejpam-6985	254	24	6.1	6.1	NUM
ejpam-6985	254	25	)	)	PUNCT
ejpam-6985	254	26	a.	a.	NOUN
ejpam-6985	254	27	ben	ben	PROPN
ejpam-6985	254	28	ahmed	ahmed	PROPN
ejpam-6985	254	29	/	/	SYM
ejpam-6985	254	30	eur	eur	PROPN
ejpam-6985	254	31	.	.	PUNCT
ejpam-6985	255	1	j.	j.	PROPN
ejpam-6985	255	2	pure	pure	PROPN
ejpam-6985	255	3	appl	appl	PROPN
ejpam-6985	255	4	.	.	PROPN
ejpam-6985	255	5	math	math	PROPN
ejpam-6985	255	6	,	,	PUNCT
ejpam-6985	255	7	18	18	NUM
ejpam-6985	255	8	(	(	PUNCT
ejpam-6985	255	9	4	4	NUM
ejpam-6985	255	10	)	)	PUNCT
ejpam-6985	255	11	(	(	PUNCT
ejpam-6985	255	12	2025	2025	NUM
ejpam-6985	255	13	)	)	PUNCT
ejpam-6985	255	14	,	,	PUNCT
ejpam-6985	255	15	6985	6985	NUM
ejpam-6985	255	16	12	12	NUM
ejpam-6985	255	17	of	of	ADP
ejpam-6985	255	18	16	16	NUM
ejpam-6985	255	19	be	be	AUX
ejpam-6985	255	20	the	the	DET
ejpam-6985	255	21	standard	standard	ADJ
ejpam-6985	255	22	cr	cr	PROPN
ejpam-6985	255	23	(	(	PUNCT
ejpam-6985	255	24	1	1	NUM
ejpam-6985	255	25	,	,	PUNCT
ejpam-6985	255	26	0	0	NUM
ejpam-6985	255	27	)	)	PUNCT
ejpam-6985	255	28	vector	vector	NOUN
ejpam-6985	255	29	field	field	NOUN
ejpam-6985	255	30	.	.	PUNCT
ejpam-6985	256	1	rossi	rossi	PROPN
ejpam-6985	256	2	’s	’s	PART
ejpam-6985	256	3	idea	idea	NOUN
ejpam-6985	256	4	is	be	AUX
ejpam-6985	256	5	to	to	PART
ejpam-6985	256	6	perturb	perturb	VERB
ejpam-6985	256	7	the	the	DET
ejpam-6985	256	8	cr	cr	PROPN
ejpam-6985	256	9	structure	structure	NOUN
ejpam-6985	256	10	by	by	ADP
ejpam-6985	256	11	adding	add	VERB
ejpam-6985	256	12	a	a	DET
ejpam-6985	256	13	small	small	ADJ
ejpam-6985	256	14	non	non	ADJ
ejpam-6985	256	15	-	-	ADJ
ejpam-6985	256	16	holomorphic	holomorphic	ADJ
ejpam-6985	256	17	component	component	NOUN
ejpam-6985	256	18	;	;	PUNCT
ejpam-6985	256	19	one	one	NUM
ejpam-6985	256	20	convenient	convenient	ADJ
ejpam-6985	256	21	model	model	NOUN
ejpam-6985	256	22	family	family	NOUN
ejpam-6985	256	23	is	be	AUX
ejpam-6985	256	24	lε	lε	ADP
ejpam-6985	256	25	=	=	PUNCT
ejpam-6985	256	26	l	l	PROPN
ejpam-6985	256	27	+	+	CCONJ
ejpam-6985	256	28	εψ(z	εψ(z	NOUN
ejpam-6985	256	29	,	,	PUNCT
ejpam-6985	256	30	z̄	z̄	X
ejpam-6985	256	31	)	)	PUNCT
ejpam-6985	256	32	∂	∂	NUM
ejpam-6985	256	33	∂zj	∂zj	NOUN
ejpam-6985	256	34	,	,	PUNCT
ejpam-6985	256	35	(	(	PUNCT
ejpam-6985	256	36	6.2	6.2	NUM
ejpam-6985	256	37	)	)	PUNCT
ejpam-6985	256	38	where	where	SCONJ
ejpam-6985	256	39	ψ	ψ	NOUN
ejpam-6985	256	40	is	be	AUX
ejpam-6985	256	41	a	a	DET
ejpam-6985	256	42	suitable	suitable	ADJ
ejpam-6985	256	43	smooth	smooth	ADJ
ejpam-6985	256	44	function	function	NOUN
ejpam-6985	256	45	and	and	CCONJ
ejpam-6985	256	46	ε	ε	PROPN
ejpam-6985	256	47	a	a	DET
ejpam-6985	256	48	small	small	ADJ
ejpam-6985	256	49	real	real	ADJ
ejpam-6985	256	50	parameter	parameter	NOUN
ejpam-6985	256	51	;	;	PUNCT
ejpam-6985	256	52	the	the	DET
ejpam-6985	256	53	precise	precise	ADJ
ejpam-6985	256	54	choice	choice	NOUN
ejpam-6985	256	55	of	of	ADP
ejpam-6985	256	56	ψ	ψ	NOUN
ejpam-6985	256	57	must	must	AUX
ejpam-6985	256	58	ensure	ensure	VERB
ejpam-6985	256	59	strict	strict	ADJ
ejpam-6985	256	60	pseudoconvexity	pseudoconvexity	NOUN
ejpam-6985	256	61	is	be	AUX
ejpam-6985	256	62	preserved	preserve	VERB
ejpam-6985	256	63	for	for	ADP
ejpam-6985	256	64	small	small	ADJ
ejpam-6985	256	65	ε	ε	PROPN
ejpam-6985	256	66	.	.	PUNCT
ejpam-6985	257	1	a	a	DET
ejpam-6985	257	2	commonly	commonly	ADV
ejpam-6985	257	3	used	use	VERB
ejpam-6985	257	4	simplified	simplified	ADJ
ejpam-6985	257	5	form	form	NOUN
ejpam-6985	257	6	is	be	AUX
ejpam-6985	257	7	lλ	lλ	NOUN
ejpam-6985	257	8	=	=	SYM
ejpam-6985	257	9	z2	z2	PROPN
ejpam-6985	257	10	∂	∂	NUM
ejpam-6985	257	11	∂z1	∂z1	PROPN
ejpam-6985	257	12	−	−	PROPN
ejpam-6985	257	13	z1	z1	NOUN
ejpam-6985	257	14	∂	∂	NUM
ejpam-6985	257	15	∂z2	∂z2	NOUN
ejpam-6985	257	16	+	+	CCONJ
ejpam-6985	257	17	λ	λ	PROPN
ejpam-6985	257	18	(	(	PUNCT
ejpam-6985	257	19	z1	z1	NOUN
ejpam-6985	257	20	∂	∂	NUM
ejpam-6985	257	21	∂z1	∂z1	PROPN
ejpam-6985	257	22	+	+	CCONJ
ejpam-6985	257	23	z2	z2	PROPN
ejpam-6985	257	24	∂	∂	NUM
ejpam-6985	257	25	∂z2	∂z2	PROPN
ejpam-6985	257	26	)	)	PUNCT
ejpam-6985	257	27	,	,	PUNCT
ejpam-6985	257	28	λ	λ	X
ejpam-6985	257	29	∈	∈	PROPN
ejpam-6985	257	30	r	r	NOUN
ejpam-6985	257	31	,	,	PUNCT
ejpam-6985	257	32	(	(	PUNCT
ejpam-6985	257	33	6.3	6.3	NUM
ejpam-6985	257	34	)	)	PUNCT
ejpam-6985	257	35	which	which	PRON
ejpam-6985	257	36	for	for	ADP
ejpam-6985	257	37	λ	λ	NOUN
ejpam-6985	257	38	=	=	NOUN
ejpam-6985	257	39	̸	̸	NUM
ejpam-6985	257	40	0	0	NUM
ejpam-6985	257	41	gives	give	VERB
ejpam-6985	257	42	an	an	DET
ejpam-6985	257	43	inequivalent	inequivalent	NOUN
ejpam-6985	257	44	cr	cr	NOUN
ejpam-6985	257	45	structure	structure	NOUN
ejpam-6985	257	46	for	for	ADP
ejpam-6985	257	47	small	small	ADJ
ejpam-6985	257	48	|λ|	|λ|	NOUN
ejpam-6985	257	49	;	;	PUNCT
ejpam-6985	257	50	see	see	VERB
ejpam-6985	257	51	[	[	X
ejpam-6985	257	52	14–16	14–16	NUM
ejpam-6985	257	53	]	]	PUNCT
ejpam-6985	257	54	for	for	ADP
ejpam-6985	257	55	constructions	construction	NOUN
ejpam-6985	257	56	and	and	CCONJ
ejpam-6985	257	57	non	non	ADJ
ejpam-6985	257	58	-	-	ADJ
ejpam-6985	257	59	embeddability	embeddability	ADJ
ejpam-6985	257	60	proofs	proof	NOUN
ejpam-6985	257	61	.	.	PUNCT
ejpam-6985	258	1	6.3	6.3	NUM
ejpam-6985	258	2	.	.	PUNCT
ejpam-6985	258	3	implications	implication	NOUN
ejpam-6985	258	4	for	for	ADP
ejpam-6985	258	5	spectral	spectral	ADJ
ejpam-6985	258	6	geometry	geometry	NOUN
ejpam-6985	258	7	the	the	DET
ejpam-6985	258	8	rossi	rossi	PROPN
ejpam-6985	258	9	family	family	NOUN
ejpam-6985	258	10	provides	provide	VERB
ejpam-6985	258	11	a	a	DET
ejpam-6985	258	12	natural	natural	ADJ
ejpam-6985	258	13	family	family	NOUN
ejpam-6985	258	14	to	to	PART
ejpam-6985	258	15	test	test	VERB
ejpam-6985	258	16	stability	stability	NOUN
ejpam-6985	258	17	of	of	ADP
ejpam-6985	258	18	the	the	DET
ejpam-6985	258	19	cheeger	cheeg	ADJ
ejpam-6985	258	20	–	–	PUNCT
ejpam-6985	258	21	cr	cr	PART
ejpam-6985	258	22	inequality	inequality	NOUN
ejpam-6985	258	23	and	and	CCONJ
ejpam-6985	258	24	the	the	DET
ejpam-6985	258	25	sensitivity	sensitivity	NOUN
ejpam-6985	258	26	of	of	ADP
ejpam-6985	258	27	λ1(∆b	λ1(∆b	NOUN
ejpam-6985	258	28	)	)	PUNCT
ejpam-6985	258	29	to	to	ADP
ejpam-6985	258	30	torsion	torsion	NOUN
ejpam-6985	258	31	and	and	CCONJ
ejpam-6985	258	32	non	non	ADJ
ejpam-6985	258	33	-	-	NOUN
ejpam-6985	258	34	embeddability	embeddability	NOUN
ejpam-6985	258	35	.	.	PUNCT
ejpam-6985	259	1	two	two	NUM
ejpam-6985	259	2	complementary	complementary	ADJ
ejpam-6985	259	3	questions	question	NOUN
ejpam-6985	259	4	arise	arise	VERB
ejpam-6985	259	5	:	:	PUNCT
ejpam-6985	259	6	(	(	PUNCT
ejpam-6985	259	7	i	i	NOUN
ejpam-6985	259	8	)	)	PUNCT
ejpam-6985	259	9	stability	stability	NOUN
ejpam-6985	259	10	:	:	PUNCT
ejpam-6985	259	11	how	how	SCONJ
ejpam-6985	259	12	does	do	AUX
ejpam-6985	259	13	λ1(∆	λ1(∆	VERB
ejpam-6985	259	14	λ	λ	PROPN
ejpam-6985	259	15	b	b	NOUN
ejpam-6985	259	16	)	)	PUNCT
ejpam-6985	259	17	vary	vary	VERB
ejpam-6985	259	18	with	with	ADP
ejpam-6985	259	19	the	the	DET
ejpam-6985	259	20	deformation	deformation	NOUN
ejpam-6985	259	21	parameter	parameter	NOUN
ejpam-6985	259	22	λ	λ	NOUN
ejpam-6985	259	23	?	?	PROPN
ejpam-6985	260	1	in	in	ADP
ejpam-6985	260	2	particular	particular	ADJ
ejpam-6985	260	3	,	,	PUNCT
ejpam-6985	260	4	does	do	AUX
ejpam-6985	260	5	the	the	DET
ejpam-6985	260	6	cheeger	cheeg	ADJ
ejpam-6985	260	7	–	–	PUNCT
ejpam-6985	260	8	cr	cr	PROPN
ejpam-6985	260	9	lower	lower	ADV
ejpam-6985	260	10	bound	bind	VERB
ejpam-6985	260	11	remain	remain	VERB
ejpam-6985	260	12	uniform	uniform	ADJ
ejpam-6985	260	13	in	in	ADP
ejpam-6985	260	14	λ	λ	PROPN
ejpam-6985	260	15	for	for	ADP
ejpam-6985	260	16	small	small	ADJ
ejpam-6985	260	17	deformations	deformation	NOUN
ejpam-6985	260	18	?	?	PUNCT
ejpam-6985	261	1	(	(	PUNCT
ejpam-6985	261	2	ii	ii	NOUN
ejpam-6985	261	3	)	)	PUNCT
ejpam-6985	261	4	detectability	detectability	NOUN
ejpam-6985	261	5	:	:	PUNCT
ejpam-6985	261	6	can	can	AUX
ejpam-6985	261	7	spectral	spectral	ADJ
ejpam-6985	261	8	data	datum	NOUN
ejpam-6985	261	9	(	(	PUNCT
ejpam-6985	261	10	e.g.	e.g.	ADV
ejpam-6985	261	11	λ1	λ1	ADJ
ejpam-6985	261	12	,	,	PUNCT
ejpam-6985	261	13	heat	heat	NOUN
ejpam-6985	261	14	trace	trace	NOUN
ejpam-6985	261	15	asymptotics	asymptotic	NOUN
ejpam-6985	261	16	)	)	PUNCT
ejpam-6985	261	17	detect	detect	NOUN
ejpam-6985	261	18	embeddability	embeddability	NOUN
ejpam-6985	261	19	or	or	CCONJ
ejpam-6985	261	20	torsion	torsion	NOUN
ejpam-6985	261	21	in	in	ADP
ejpam-6985	261	22	the	the	DET
ejpam-6985	261	23	cr	cr	PROPN
ejpam-6985	261	24	structure	structure	NOUN
ejpam-6985	261	25	?	?	PUNCT
ejpam-6985	262	1	proposition	proposition	NOUN
ejpam-6985	262	2	7	7	NUM
ejpam-6985	262	3	(	(	PUNCT
ejpam-6985	262	4	first	first	ADJ
ejpam-6985	262	5	-	-	PUNCT
ejpam-6985	262	6	order	order	NOUN
ejpam-6985	262	7	spectral	spectral	ADJ
ejpam-6985	262	8	perturbation	perturbation	NOUN
ejpam-6985	262	9	for	for	ADP
ejpam-6985	262	10	simple	simple	ADJ
ejpam-6985	262	11	eigenvalues	eigenvalue	NOUN
ejpam-6985	262	12	)	)	PUNCT
ejpam-6985	262	13	.	.	PUNCT
ejpam-6985	263	1	let	let	VERB
ejpam-6985	263	2	{	{	PUNCT
ejpam-6985	263	3	∆λ	∆λ	NOUN
ejpam-6985	263	4	b	b	PROPN
ejpam-6985	263	5	}	}	PUNCT
ejpam-6985	263	6	λ∈(−λ0,λ0	λ∈(−λ0,λ0	PUNCT
ejpam-6985	263	7	)	)	PUNCT
ejpam-6985	263	8	be	be	AUX
ejpam-6985	263	9	a	a	DET
ejpam-6985	263	10	c1	c1	NOUN
ejpam-6985	263	11	-	-	PUNCT
ejpam-6985	263	12	family	family	NOUN
ejpam-6985	263	13	of	of	ADP
ejpam-6985	263	14	self	self	NOUN
ejpam-6985	263	15	-	-	PUNCT
ejpam-6985	263	16	adjoint	adjoint	NOUN
ejpam-6985	263	17	realizations	realization	NOUN
ejpam-6985	263	18	of	of	ADP
ejpam-6985	263	19	the	the	DET
ejpam-6985	263	20	sub	sub	NOUN
ejpam-6985	263	21	-	-	NOUN
ejpam-6985	263	22	laplacian	laplacian	ADJ
ejpam-6985	263	23	on	on	ADP
ejpam-6985	263	24	a	a	DET
ejpam-6985	263	25	fixed	fix	VERB
ejpam-6985	263	26	compact	compact	ADJ
ejpam-6985	263	27	manifold	manifold	ADJ
ejpam-6985	263	28	m	m	NOUN
ejpam-6985	263	29	,	,	PUNCT
ejpam-6985	263	30	acting	act	VERB
ejpam-6985	263	31	on	on	ADP
ejpam-6985	263	32	the	the	DET
ejpam-6985	263	33	fixed	fix	VERB
ejpam-6985	263	34	hilbert	hilbert	NOUN
ejpam-6985	263	35	space	space	NOUN
ejpam-6985	263	36	l2(m,µ	l2(m,µ	NOUN
ejpam-6985	263	37	)	)	PUNCT
ejpam-6985	263	38	,	,	PUNCT
ejpam-6985	263	39	where	where	SCONJ
ejpam-6985	263	40	µ	µ	NOUN
ejpam-6985	263	41	is	be	AUX
ejpam-6985	263	42	a	a	DET
ejpam-6985	263	43	fixed	fix	VERB
ejpam-6985	263	44	smooth	smooth	ADJ
ejpam-6985	263	45	reference	reference	NOUN
ejpam-6985	263	46	measure	measure	NOUN
ejpam-6985	263	47	.	.	PUNCT
ejpam-6985	264	1	assume	assume	VERB
ejpam-6985	264	2	:	:	PUNCT
ejpam-6985	264	3	(	(	PUNCT
ejpam-6985	264	4	i	i	NOUN
ejpam-6985	264	5	)	)	PUNCT
ejpam-6985	264	6	each	each	DET
ejpam-6985	264	7	∆λ	∆λ	PROPN
ejpam-6985	264	8	b	b	PROPN
ejpam-6985	264	9	has	have	VERB
ejpam-6985	264	10	compact	compact	ADJ
ejpam-6985	264	11	resolvent	resolvent	NOUN
ejpam-6985	264	12	on	on	ADP
ejpam-6985	264	13	l2(m,µ	l2(m,µ	NOUN
ejpam-6985	264	14	)	)	PUNCT
ejpam-6985	264	15	;	;	PUNCT
ejpam-6985	264	16	(	(	PUNCT
ejpam-6985	264	17	ii	ii	X
ejpam-6985	264	18	)	)	PUNCT
ejpam-6985	264	19	the	the	DET
ejpam-6985	264	20	dependence	dependence	NOUN
ejpam-6985	264	21	λ	λ	NOUN
ejpam-6985	264	22	7→	7→	NOUN
ejpam-6985	264	23	∆λ	∆λ	PROPN
ejpam-6985	264	24	b	b	PROPN
ejpam-6985	264	25	is	be	AUX
ejpam-6985	264	26	c1	c1	NOUN
ejpam-6985	264	27	in	in	ADP
ejpam-6985	264	28	the	the	DET
ejpam-6985	264	29	sense	sense	NOUN
ejpam-6985	264	30	of	of	ADP
ejpam-6985	264	31	graph	graph	NOUN
ejpam-6985	264	32	-	-	PUNCT
ejpam-6985	264	33	norm	norm	NOUN
ejpam-6985	264	34	bounded	bounded	ADJ
ejpam-6985	264	35	operators	operator	NOUN
ejpam-6985	264	36	on	on	ADP
ejpam-6985	264	37	a	a	DET
ejpam-6985	264	38	common	common	ADJ
ejpam-6985	264	39	dense	dense	ADJ
ejpam-6985	264	40	domain	domain	NOUN
ejpam-6985	264	41	d	d	NOUN
ejpam-6985	264	42	(	(	PUNCT
ejpam-6985	264	43	see	see	INTJ
ejpam-6985	264	44	remark	remark	NOUN
ejpam-6985	264	45	4	4	NUM
ejpam-6985	264	46	below	below	ADV
ejpam-6985	264	47	)	)	PUNCT
ejpam-6985	264	48	;	;	PUNCT
ejpam-6985	264	49	(	(	PUNCT
ejpam-6985	264	50	iii	iii	X
ejpam-6985	264	51	)	)	PUNCT
ejpam-6985	264	52	λ1(0	λ1(0	PROPN
ejpam-6985	264	53	)	)	PUNCT
ejpam-6985	264	54	is	be	AUX
ejpam-6985	264	55	a	a	DET
ejpam-6985	264	56	simple	simple	ADJ
ejpam-6985	264	57	eigenvalue	eigenvalue	NOUN
ejpam-6985	264	58	with	with	ADP
ejpam-6985	264	59	normalized	normalize	VERB
ejpam-6985	264	60	real	real	ADV
ejpam-6985	264	61	-	-	PUNCT
ejpam-6985	264	62	valued	value	VERB
ejpam-6985	264	63	eigenfunction	eigenfunction	NOUN
ejpam-6985	264	64	ϕ0	ϕ0	NOUN
ejpam-6985	264	65	∈	∈	PROPN
ejpam-6985	264	66	d	d	NOUN
ejpam-6985	264	67	,	,	PUNCT
ejpam-6985	264	68	∥ϕ0∥l2(µ	∥ϕ0∥l2(µ	PROPN
ejpam-6985	264	69	)	)	PUNCT
ejpam-6985	264	70	=	=	SYM
ejpam-6985	265	1	1	1	X
ejpam-6985	265	2	.	.	PUNCT
ejpam-6985	265	3	then	then	ADV
ejpam-6985	265	4	there	there	PRON
ejpam-6985	265	5	exist	exist	VERB
ejpam-6985	265	6	c1	c1	NOUN
ejpam-6985	265	7	maps	map	VERB
ejpam-6985	265	8	λ	λ	PROPN
ejpam-6985	265	9	7→	7→	NUM
ejpam-6985	265	10	λ1(λ	λ1(λ	NOUN
ejpam-6985	265	11	)	)	PUNCT
ejpam-6985	265	12	and	and	CCONJ
ejpam-6985	265	13	λ	λ	X
ejpam-6985	265	14	7→	7→	NUM
ejpam-6985	265	15	ϕλ	ϕλ	DET
ejpam-6985	265	16	∈	∈	PROPN
ejpam-6985	265	17	d	d	NOUN
ejpam-6985	265	18	with	with	ADP
ejpam-6985	265	19	∆λ	∆λ	PROPN
ejpam-6985	265	20	bϕλ	bϕλ	NOUN
ejpam-6985	265	21	=	=	SYM
ejpam-6985	265	22	λ1(λ)ϕλ	λ1(λ)ϕλ	NOUN
ejpam-6985	265	23	,	,	PUNCT
ejpam-6985	265	24	∥ϕλ∥l2(µ	∥ϕλ∥l2(µ	PROPN
ejpam-6985	265	25	)	)	PUNCT
ejpam-6985	265	26	=	=	SYM
ejpam-6985	266	1	1	1	NUM
ejpam-6985	266	2	,	,	PUNCT
ejpam-6985	266	3	ϕ0	ϕ0	NOUN
ejpam-6985	266	4	=	=	SYM
ejpam-6985	266	5	ϕλ	ϕλ	X
ejpam-6985	266	6	∣∣	∣∣	X
ejpam-6985	266	7	λ=0	λ=0	X
ejpam-6985	266	8	and	and	CCONJ
ejpam-6985	266	9	the	the	DET
ejpam-6985	266	10	first	first	ADJ
ejpam-6985	266	11	derivative	derivative	NOUN
ejpam-6985	266	12	at	at	ADP
ejpam-6985	266	13	λ	λ	X
ejpam-6985	266	14	=	=	SYM
ejpam-6985	266	15	0	0	NUM
ejpam-6985	266	16	satisfies	satisfy	VERB
ejpam-6985	266	17	the	the	DET
ejpam-6985	266	18	hellmann	hellmann	PROPN
ejpam-6985	266	19	–	–	PUNCT
ejpam-6985	266	20	feynman	feynman	PROPN
ejpam-6985	266	21	identity	identity	NOUN
ejpam-6985	266	22	d	d	X
ejpam-6985	266	23	dλ	dλ	NOUN
ejpam-6985	266	24	∣∣∣	∣∣∣	NOUN
ejpam-6985	266	25	λ=0	λ=0	X
ejpam-6985	266	26	λ1(λ	λ1(λ	PROPN
ejpam-6985	266	27	)	)	PUNCT
ejpam-6985	266	28	=	=	PUNCT
ejpam-6985	266	29	〈	〈	PROPN
ejpam-6985	266	30	∆̇0	∆̇0	PROPN
ejpam-6985	266	31	bϕ0	bϕ0	VERB
ejpam-6985	266	32	,	,	PUNCT
ejpam-6985	266	33	ϕ0	ϕ0	NOUN
ejpam-6985	266	34	〉	〉	NOUN
ejpam-6985	266	35	l2(m,µ	l2(m,µ	NOUN
ejpam-6985	266	36	)	)	PUNCT
ejpam-6985	266	37	,	,	PUNCT
ejpam-6985	266	38	(	(	PUNCT
ejpam-6985	266	39	6.4	6.4	NUM
ejpam-6985	266	40	)	)	PUNCT
ejpam-6985	266	41	where	where	SCONJ
ejpam-6985	266	42	∆̇0	∆̇0	PROPN
ejpam-6985	266	43	b	b	PROPN
ejpam-6985	266	44	:	:	PUNCT
ejpam-6985	267	1	=	=	SYM
ejpam-6985	267	2	d	d	SYM
ejpam-6985	267	3	dλ	dλ	NOUN
ejpam-6985	268	1	∣∣	∣∣	X
ejpam-6985	268	2	λ=0	λ=0	PROPN
ejpam-6985	268	3	∆λ	∆λ	PROPN
ejpam-6985	268	4	b	b	PROPN
ejpam-6985	268	5	exists	exist	VERB
ejpam-6985	268	6	as	as	ADP
ejpam-6985	268	7	a	a	DET
ejpam-6985	268	8	symmetric	symmetric	ADJ
ejpam-6985	268	9	operator	operator	NOUN
ejpam-6985	268	10	on	on	ADP
ejpam-6985	268	11	d.	d.	PROPN
ejpam-6985	268	12	a.	a.	PROPN
ejpam-6985	268	13	ben	ben	PROPN
ejpam-6985	268	14	ahmed	ahmed	PROPN
ejpam-6985	268	15	/	/	SYM
ejpam-6985	268	16	eur	eur	PROPN
ejpam-6985	268	17	.	.	PUNCT
ejpam-6985	269	1	j.	j.	PROPN
ejpam-6985	269	2	pure	pure	PROPN
ejpam-6985	269	3	appl	appl	PROPN
ejpam-6985	269	4	.	.	PROPN
ejpam-6985	269	5	math	math	PROPN
ejpam-6985	269	6	,	,	PUNCT
ejpam-6985	269	7	18	18	NUM
ejpam-6985	269	8	(	(	PUNCT
ejpam-6985	269	9	4	4	NUM
ejpam-6985	269	10	)	)	PUNCT
ejpam-6985	269	11	(	(	PUNCT
ejpam-6985	269	12	2025	2025	NUM
ejpam-6985	269	13	)	)	PUNCT
ejpam-6985	269	14	,	,	PUNCT
ejpam-6985	269	15	6985	6985	NUM
ejpam-6985	269	16	13	13	NUM
ejpam-6985	269	17	of	of	ADP
ejpam-6985	269	18	16	16	NUM
ejpam-6985	269	19	proof	proof	NOUN
ejpam-6985	269	20	.	.	PUNCT
ejpam-6985	270	1	step	step	NOUN
ejpam-6985	270	2	1	1	NUM
ejpam-6985	270	3	:	:	PUNCT
ejpam-6985	270	4	simple	simple	ADJ
ejpam-6985	270	5	eigenvalue	eigenvalue	NOUN
ejpam-6985	270	6	branch	branch	NOUN
ejpam-6985	270	7	and	and	CCONJ
ejpam-6985	270	8	differentiability	differentiability	NOUN
ejpam-6985	270	9	.	.	PUNCT
ejpam-6985	271	1	by	by	ADP
ejpam-6985	271	2	(	(	PUNCT
ejpam-6985	271	3	i	i	NOUN
ejpam-6985	271	4	)	)	PUNCT
ejpam-6985	271	5	the	the	DET
ejpam-6985	271	6	spectrum	spectrum	NOUN
ejpam-6985	271	7	of	of	ADP
ejpam-6985	271	8	∆λ	∆λ	PROPN
ejpam-6985	271	9	b	b	PROPN
ejpam-6985	271	10	is	be	AUX
ejpam-6985	271	11	pure	pure	ADJ
ejpam-6985	271	12	point	point	NOUN
ejpam-6985	271	13	with	with	ADP
ejpam-6985	271	14	finite	finite	PROPN
ejpam-6985	271	15	multiplicities	multiplicity	NOUN
ejpam-6985	271	16	accumulating	accumulate	VERB
ejpam-6985	271	17	only	only	ADV
ejpam-6985	271	18	at	at	ADP
ejpam-6985	271	19	+	+	ADV
ejpam-6985	271	20	∞.	∞.	PROPN
ejpam-6985	271	21	by	by	ADP
ejpam-6985	271	22	(	(	PUNCT
ejpam-6985	271	23	ii	ii	NOUN
ejpam-6985	271	24	)	)	PUNCT
ejpam-6985	271	25	and	and	CCONJ
ejpam-6985	271	26	classical	classical	ADJ
ejpam-6985	271	27	kato	kato	PROPN
ejpam-6985	271	28	theory	theory	NOUN
ejpam-6985	271	29	(	(	PUNCT
ejpam-6985	271	30	see	see	VERB
ejpam-6985	271	31	[	[	X
ejpam-6985	271	32	17	17	NUM
ejpam-6985	271	33	,	,	PUNCT
ejpam-6985	271	34	ch	ch	PROPN
ejpam-6985	271	35	.	.	PROPN
ejpam-6985	271	36	ii	ii	PROPN
ejpam-6985	271	37	,	,	PUNCT
ejpam-6985	271	38	thm	thm	PROPN
ejpam-6985	271	39	.	.	PUNCT
ejpam-6985	272	1	5.8	5.8	NUM
ejpam-6985	272	2	;	;	PUNCT
ejpam-6985	272	3	ch	ch	NOUN
ejpam-6985	272	4	.	.	PUNCT
ejpam-6985	272	5	vii	vii	PROPN
ejpam-6985	272	6	,	,	PUNCT
ejpam-6985	272	7	§	§	PROPN
ejpam-6985	272	8	3	3	NUM
ejpam-6985	272	9	]	]	NUM
ejpam-6985	272	10	)	)	PUNCT
ejpam-6985	272	11	,	,	PUNCT
ejpam-6985	272	12	the	the	DET
ejpam-6985	272	13	isolated	isolated	ADJ
ejpam-6985	272	14	simple	simple	ADJ
ejpam-6985	272	15	eigenvalue	eigenvalue	PROPN
ejpam-6985	272	16	λ1(0	λ1(0	PROPN
ejpam-6985	272	17	)	)	PUNCT
ejpam-6985	272	18	admits	admit	VERB
ejpam-6985	272	19	a	a	DET
ejpam-6985	272	20	unique	unique	ADJ
ejpam-6985	272	21	c1	c1	NOUN
ejpam-6985	272	22	continuation	continuation	NOUN
ejpam-6985	272	23	λ	λ	PROPN
ejpam-6985	272	24	7→	7→	NUM
ejpam-6985	272	25	λ1(λ	λ1(λ	NOUN
ejpam-6985	272	26	)	)	PUNCT
ejpam-6985	272	27	and	and	CCONJ
ejpam-6985	272	28	a	a	DET
ejpam-6985	272	29	c1	c1	PROPN
ejpam-6985	272	30	choice	choice	NOUN
ejpam-6985	272	31	of	of	ADP
ejpam-6985	272	32	normalized	normalize	VERB
ejpam-6985	272	33	eigenvectors	eigenvector	NOUN
ejpam-6985	272	34	λ	λ	X
ejpam-6985	272	35	7→	7→	NUM
ejpam-6985	272	36	ϕλ	ϕλ	PRON
ejpam-6985	272	37	∈	∈	NOUN
ejpam-6985	273	1	d	d	NOUN
ejpam-6985	273	2	satisfying	satisfy	VERB
ejpam-6985	273	3	∆λ	∆λ	PROPN
ejpam-6985	273	4	bϕλ	bϕλ	NOUN
ejpam-6985	273	5	=	=	SYM
ejpam-6985	273	6	λ1(λ)ϕλ	λ1(λ)ϕλ	NOUN
ejpam-6985	273	7	,	,	PUNCT
ejpam-6985	273	8	∥ϕλ∥l2(µ	∥ϕλ∥l2(µ	PROPN
ejpam-6985	273	9	)	)	PUNCT
ejpam-6985	273	10	=	=	SYM
ejpam-6985	274	1	1	1	X
ejpam-6985	274	2	.	.	PUNCT
ejpam-6985	274	3	(	(	PUNCT
ejpam-6985	274	4	6.5	6.5	NUM
ejpam-6985	274	5	)	)	PUNCT
ejpam-6985	274	6	step	step	NOUN
ejpam-6985	274	7	2	2	NUM
ejpam-6985	274	8	:	:	PUNCT
ejpam-6985	274	9	gauge	gauge	NOUN
ejpam-6985	274	10	choice	choice	NOUN
ejpam-6985	274	11	.	.	PUNCT
ejpam-6985	275	1	differentiability	differentiability	NOUN
ejpam-6985	275	2	of	of	ADP
ejpam-6985	275	3	ϕλ	ϕλ	PRON
ejpam-6985	275	4	is	be	AUX
ejpam-6985	275	5	not	not	PART
ejpam-6985	275	6	unique	unique	ADJ
ejpam-6985	275	7	up	up	ADP
ejpam-6985	275	8	to	to	ADP
ejpam-6985	275	9	a	a	DET
ejpam-6985	275	10	λ	λ	NOUN
ejpam-6985	275	11	-	-	ADJ
ejpam-6985	275	12	dependent	dependent	ADJ
ejpam-6985	275	13	phase	phase	NOUN
ejpam-6985	275	14	.	.	PUNCT
ejpam-6985	276	1	fix	fix	VERB
ejpam-6985	276	2	the	the	DET
ejpam-6985	276	3	parallel	parallel	ADJ
ejpam-6985	276	4	transport	transport	NOUN
ejpam-6985	276	5	gauge	gauge	NOUN
ejpam-6985	276	6	⟨ϕ̇λ	⟨ϕ̇λ	NOUN
ejpam-6985	276	7	,	,	PUNCT
ejpam-6985	276	8	ϕλ⟩l2(µ	ϕλ⟩l2(µ	PROPN
ejpam-6985	276	9	)	)	PUNCT
ejpam-6985	276	10	=	=	SYM
ejpam-6985	276	11	0	0	NUM
ejpam-6985	276	12	for	for	ADP
ejpam-6985	276	13	all	all	DET
ejpam-6985	276	14	λ	λ	NOUN
ejpam-6985	276	15	,	,	PUNCT
ejpam-6985	276	16	(	(	PUNCT
ejpam-6985	276	17	6.6	6.6	NUM
ejpam-6985	276	18	)	)	PUNCT
ejpam-6985	276	19	where	where	SCONJ
ejpam-6985	276	20	dot	dot	NOUN
ejpam-6985	276	21	denotes	denote	NOUN
ejpam-6985	276	22	d	d	X
ejpam-6985	276	23	dλ	dλ	INTJ
ejpam-6985	276	24	.	.	PUNCT
ejpam-6985	277	1	this	this	PRON
ejpam-6985	277	2	can	can	AUX
ejpam-6985	277	3	always	always	ADV
ejpam-6985	277	4	be	be	AUX
ejpam-6985	277	5	achieved	achieve	VERB
ejpam-6985	277	6	by	by	ADP
ejpam-6985	277	7	multiplying	multiply	VERB
ejpam-6985	277	8	ϕλ	ϕλ	NOUN
ejpam-6985	277	9	by	by	ADP
ejpam-6985	277	10	a	a	DET
ejpam-6985	277	11	suitable	suitable	ADJ
ejpam-6985	277	12	c1	c1	NOUN
ejpam-6985	277	13	real	real	ADJ
ejpam-6985	277	14	phase	phase	NOUN
ejpam-6985	277	15	factor	factor	NOUN
ejpam-6985	277	16	.	.	PUNCT
ejpam-6985	278	1	in	in	ADP
ejpam-6985	278	2	particular	particular	ADJ
ejpam-6985	278	3	at	at	ADP
ejpam-6985	278	4	λ	λ	X
ejpam-6985	278	5	=	=	SYM
ejpam-6985	278	6	0	0	NUM
ejpam-6985	278	7	we	we	PRON
ejpam-6985	278	8	have	have	VERB
ejpam-6985	278	9	⟨ϕ̇0	⟨ϕ̇0	NOUN
ejpam-6985	278	10	,	,	PUNCT
ejpam-6985	278	11	ϕ0⟩	ϕ0⟩	PUNCT
ejpam-6985	279	1	=	=	NOUN
ejpam-6985	279	2	0	0	X
ejpam-6985	279	3	.	.	PUNCT
ejpam-6985	280	1	(	(	PUNCT
ejpam-6985	280	2	6.7	6.7	NUM
ejpam-6985	280	3	)	)	PUNCT
ejpam-6985	280	4	step	step	NOUN
ejpam-6985	280	5	3	3	NUM
ejpam-6985	280	6	:	:	PUNCT
ejpam-6985	280	7	differentiate	differentiate	VERB
ejpam-6985	280	8	the	the	DET
ejpam-6985	280	9	eigenvalue	eigenvalue	PROPN
ejpam-6985	280	10	equation	equation	NOUN
ejpam-6985	280	11	.	.	PUNCT
ejpam-6985	281	1	differentiate	differentiate	VERB
ejpam-6985	281	2	(	(	PUNCT
ejpam-6985	281	3	6.5	6.5	NUM
ejpam-6985	281	4	)	)	PUNCT
ejpam-6985	281	5	at	at	ADP
ejpam-6985	281	6	λ	λ	X
ejpam-6985	281	7	=	=	SYM
ejpam-6985	281	8	0	0	NUM
ejpam-6985	281	9	in	in	ADP
ejpam-6985	281	10	l2(m,µ	l2(m,µ	NOUN
ejpam-6985	281	11	):	):	PUNCT
ejpam-6985	281	12	∆̇0	∆̇0	PROPN
ejpam-6985	281	13	b	b	PROPN
ejpam-6985	281	14	ϕ0	ϕ0	PROPN
ejpam-6985	281	15	+	+	CCONJ
ejpam-6985	281	16	∆0	∆0	NUM
ejpam-6985	281	17	b	b	NOUN
ejpam-6985	282	1	ϕ̇0	ϕ̇0	NOUN
ejpam-6985	282	2	=	=	PUNCT
ejpam-6985	283	1	λ̇1(0)ϕ0	λ̇1(0)ϕ0	X
ejpam-6985	283	2	+	+	PUNCT
ejpam-6985	283	3	λ1(0	λ1(0	PROPN
ejpam-6985	283	4	)	)	PUNCT
ejpam-6985	284	1	ϕ̇0	ϕ̇0	AUX
ejpam-6985	284	2	.	.	PUNCT
ejpam-6985	284	3	take	take	VERB
ejpam-6985	284	4	the	the	DET
ejpam-6985	284	5	l2(µ	l2(µ	NOUN
ejpam-6985	284	6	)	)	PUNCT
ejpam-6985	284	7	inner	inner	ADJ
ejpam-6985	284	8	product	product	NOUN
ejpam-6985	284	9	with	with	ADP
ejpam-6985	284	10	ϕ0	ϕ0	NOUN
ejpam-6985	284	11	and	and	CCONJ
ejpam-6985	284	12	use	use	VERB
ejpam-6985	284	13	self	self	NOUN
ejpam-6985	284	14	-	-	PUNCT
ejpam-6985	284	15	adjointness	adjointness	NOUN
ejpam-6985	284	16	of	of	ADP
ejpam-6985	284	17	∆0	∆0	NUM
ejpam-6985	284	18	b	b	NOUN
ejpam-6985	284	19	:	:	PUNCT
ejpam-6985	284	20	〈	〈	PROPN
ejpam-6985	284	21	∆̇0	∆̇0	PROPN
ejpam-6985	284	22	b	b	PROPN
ejpam-6985	284	23	ϕ0	ϕ0	NOUN
ejpam-6985	284	24	,	,	PUNCT
ejpam-6985	284	25	ϕ0	ϕ0	NOUN
ejpam-6985	284	26	〉	〉	NOUN
ejpam-6985	284	27	+	+	CCONJ
ejpam-6985	284	28	〈	〈	PROPN
ejpam-6985	284	29	∆0	∆0	NUM
ejpam-6985	284	30	b	b	X
ejpam-6985	284	31	ϕ̇0	ϕ̇0	NOUN
ejpam-6985	284	32	,	,	PUNCT
ejpam-6985	284	33	ϕ0	ϕ0	NOUN
ejpam-6985	284	34	〉	〉	NOUN
ejpam-6985	284	35	=	=	SYM
ejpam-6985	284	36	λ̇1(0	λ̇1(0	PROPN
ejpam-6985	284	37	)	)	PUNCT
ejpam-6985	284	38	⟨ϕ0	⟨ϕ0	NOUN
ejpam-6985	284	39	,	,	PUNCT
ejpam-6985	284	40	ϕ0⟩︸	ϕ0⟩︸	PROPN
ejpam-6985	284	41	︷︷	︷︷	PROPN
ejpam-6985	284	42	︸	︸	X
ejpam-6985	285	1	=	=	NOUN
ejpam-6985	285	2	1	1	NUM
ejpam-6985	285	3	+	+	CCONJ
ejpam-6985	285	4	λ1(0	λ1(0	PROPN
ejpam-6985	285	5	)	)	PUNCT
ejpam-6985	285	6	⟨ϕ̇0	⟨ϕ̇0	PROPN
ejpam-6985	285	7	,	,	PUNCT
ejpam-6985	285	8	ϕ0⟩.	ϕ0⟩.	VERB
ejpam-6985	285	9	since	since	SCONJ
ejpam-6985	285	10	∆0	∆0	NUM
ejpam-6985	285	11	b	b	NOUN
ejpam-6985	285	12	is	be	AUX
ejpam-6985	285	13	self	self	NOUN
ejpam-6985	285	14	-	-	PUNCT
ejpam-6985	285	15	adjoint	adjoint	NOUN
ejpam-6985	285	16	and	and	CCONJ
ejpam-6985	285	17	∆0	∆0	PRON
ejpam-6985	285	18	bϕ0	bϕ0	VERB
ejpam-6985	285	19	=	=	SYM
ejpam-6985	285	20	λ1(0)ϕ0	λ1(0)ϕ0	PROPN
ejpam-6985	285	21	,	,	PUNCT
ejpam-6985	285	22	〈	〈	PROPN
ejpam-6985	285	23	∆0	∆0	NUM
ejpam-6985	285	24	b	b	X
ejpam-6985	286	1	ϕ̇0	ϕ̇0	NOUN
ejpam-6985	286	2	,	,	PUNCT
ejpam-6985	286	3	ϕ0	ϕ0	NOUN
ejpam-6985	286	4	〉	〉	NOUN
ejpam-6985	286	5	=	=	SYM
ejpam-6985	286	6	〈	〈	PROPN
ejpam-6985	286	7	ϕ̇0	ϕ̇0	PROPN
ejpam-6985	286	8	,	,	PUNCT
ejpam-6985	286	9	∆	∆	PROPN
ejpam-6985	286	10	0	0	X
ejpam-6985	287	1	bϕ0	bϕ0	VERB
ejpam-6985	287	2	〉	〉	NOUN
ejpam-6985	287	3	=	=	SYM
ejpam-6985	287	4	λ1(0	λ1(0	PROPN
ejpam-6985	287	5	)	)	PUNCT
ejpam-6985	287	6	⟨ϕ̇0	⟨ϕ̇0	PROPN
ejpam-6985	287	7	,	,	PUNCT
ejpam-6985	287	8	ϕ0⟩.	ϕ0⟩.	VERB
ejpam-6985	287	9	by	by	ADP
ejpam-6985	287	10	the	the	DET
ejpam-6985	287	11	gauge	gauge	ADJ
ejpam-6985	287	12	condition	condition	NOUN
ejpam-6985	287	13	(	(	PUNCT
ejpam-6985	287	14	6.7	6.7	NUM
ejpam-6985	287	15	)	)	PUNCT
ejpam-6985	287	16	these	these	DET
ejpam-6985	287	17	terms	term	NOUN
ejpam-6985	287	18	cancel	cancel	VERB
ejpam-6985	287	19	.	.	PUNCT
ejpam-6985	288	1	therefore	therefore	ADV
ejpam-6985	288	2	〈	〈	PROPN
ejpam-6985	288	3	∆̇0	∆̇0	PROPN
ejpam-6985	288	4	b	b	PROPN
ejpam-6985	288	5	ϕ0	ϕ0	NOUN
ejpam-6985	288	6	,	,	PUNCT
ejpam-6985	288	7	ϕ0	ϕ0	NOUN
ejpam-6985	288	8	〉	〉	NOUN
ejpam-6985	288	9	=	=	SYM
ejpam-6985	288	10	λ̇1(0	λ̇1(0	NOUN
ejpam-6985	288	11	)	)	PUNCT
ejpam-6985	288	12	,	,	PUNCT
ejpam-6985	288	13	which	which	PRON
ejpam-6985	288	14	is	be	AUX
ejpam-6985	288	15	precisely	precisely	ADV
ejpam-6985	288	16	(	(	PUNCT
ejpam-6985	288	17	6.4	6.4	NUM
ejpam-6985	288	18	)	)	PUNCT
ejpam-6985	288	19	.	.	PUNCT
ejpam-6985	289	1	step	step	NOUN
ejpam-6985	289	2	4	4	NUM
ejpam-6985	289	3	:	:	PUNCT
ejpam-6985	289	4	alternative	alternative	ADJ
ejpam-6985	289	5	derivation	derivation	NOUN
ejpam-6985	289	6	via	via	ADP
ejpam-6985	289	7	rayleigh	rayleigh	PROPN
ejpam-6985	289	8	quotient	quotient	PROPN
ejpam-6985	289	9	.	.	PUNCT
ejpam-6985	290	1	for	for	ADP
ejpam-6985	290	2	completeness	completeness	NOUN
ejpam-6985	290	3	,	,	PUNCT
ejpam-6985	290	4	we	we	PRON
ejpam-6985	290	5	give	give	VERB
ejpam-6985	290	6	a	a	DET
ejpam-6985	290	7	form	form	NOUN
ejpam-6985	290	8	-	-	PUNCT
ejpam-6985	290	9	theoretic	theoretic	NOUN
ejpam-6985	290	10	argument	argument	NOUN
ejpam-6985	290	11	which	which	PRON
ejpam-6985	290	12	is	be	AUX
ejpam-6985	290	13	often	often	ADV
ejpam-6985	290	14	convenient	convenient	ADJ
ejpam-6985	290	15	in	in	ADP
ejpam-6985	290	16	cr	cr	PROPN
ejpam-6985	290	17	geometry	geometry	NOUN
ejpam-6985	290	18	.	.	PUNCT
ejpam-6985	291	1	assume	assume	VERB
ejpam-6985	291	2	each	each	DET
ejpam-6985	291	3	∆λ	∆λ	PROPN
ejpam-6985	291	4	b	b	PROPN
ejpam-6985	291	5	is	be	AUX
ejpam-6985	291	6	associated	associate	VERB
ejpam-6985	291	7	with	with	ADP
ejpam-6985	291	8	a	a	DET
ejpam-6985	291	9	symmetric	symmetric	ADJ
ejpam-6985	291	10	closed	closed	ADJ
ejpam-6985	291	11	quadratic	quadratic	ADJ
ejpam-6985	291	12	form	form	NOUN
ejpam-6985	291	13	aλ	aλ	VERB
ejpam-6985	291	14	on	on	ADP
ejpam-6985	291	15	a	a	DET
ejpam-6985	291	16	common	common	ADJ
ejpam-6985	291	17	dense	dense	ADJ
ejpam-6985	291	18	form	form	NOUN
ejpam-6985	291	19	domain	domain	NOUN
ejpam-6985	291	20	v	v	NOUN
ejpam-6985	291	21	(	(	PUNCT
ejpam-6985	291	22	e.g.	e.g.	ADV
ejpam-6985	291	23	v	v	NOUN
ejpam-6985	291	24	=	=	NOUN
ejpam-6985	291	25	w	w	NOUN
ejpam-6985	291	26	1,2	1,2	NUM
ejpam-6985	291	27	h	h	NOUN
ejpam-6985	291	28	(	(	PUNCT
ejpam-6985	291	29	m	m	NOUN
ejpam-6985	291	30	)	)	PUNCT
ejpam-6985	291	31	)	)	PUNCT
ejpam-6985	291	32	and	and	CCONJ
ejpam-6985	292	1	that	that	SCONJ
ejpam-6985	292	2	λ	λ	PROPN
ejpam-6985	292	3	7→	7→	PROPN
ejpam-6985	292	4	aλ	aλ	ADP
ejpam-6985	292	5	is	be	AUX
ejpam-6985	292	6	c1	c1	PROPN
ejpam-6985	292	7	in	in	ADP
ejpam-6985	292	8	the	the	DET
ejpam-6985	292	9	sense	sense	NOUN
ejpam-6985	292	10	ȧ0(u	ȧ0(u	PROPN
ejpam-6985	292	11	,	,	PUNCT
ejpam-6985	292	12	v	v	NOUN
ejpam-6985	292	13	)	)	PUNCT
ejpam-6985	292	14	:	:	PUNCT
ejpam-6985	293	1	=	=	SYM
ejpam-6985	293	2	d	d	X
ejpam-6985	293	3	dλ	dλ	NOUN
ejpam-6985	293	4	∣∣∣	∣∣∣	NOUN
ejpam-6985	293	5	λ=0	λ=0	X
ejpam-6985	293	6	aλ(u	aλ(u	NUM
ejpam-6985	293	7	,	,	PUNCT
ejpam-6985	293	8	v	v	NOUN
ejpam-6985	293	9	)	)	PUNCT
ejpam-6985	293	10	exists	exist	VERB
ejpam-6985	293	11	for	for	ADP
ejpam-6985	293	12	all	all	DET
ejpam-6985	293	13	u	u	NOUN
ejpam-6985	293	14	,	,	PUNCT
ejpam-6985	293	15	v	v	NOUN
ejpam-6985	293	16	∈	∈	PROPN
ejpam-6985	293	17	v.	v.	CCONJ
ejpam-6985	293	18	for	for	ADP
ejpam-6985	293	19	the	the	DET
ejpam-6985	293	20	normalized	normalize	VERB
ejpam-6985	293	21	eigenbranch	eigenbranch	NOUN
ejpam-6985	293	22	(	(	PUNCT
ejpam-6985	293	23	λ1(λ	λ1(λ	X
ejpam-6985	293	24	)	)	PUNCT
ejpam-6985	293	25	,	,	PUNCT
ejpam-6985	293	26	ϕλ	ϕλ	X
ejpam-6985	293	27	)	)	PUNCT
ejpam-6985	293	28	one	one	NOUN
ejpam-6985	293	29	has	have	VERB
ejpam-6985	293	30	the	the	DET
ejpam-6985	293	31	rayleigh	rayleigh	PROPN
ejpam-6985	293	32	identity	identity	NOUN
ejpam-6985	293	33	λ1(λ	λ1(λ	PROPN
ejpam-6985	293	34	)	)	PUNCT
ejpam-6985	293	35	=	=	SYM
ejpam-6985	293	36	aλ(ϕλ	aλ(ϕλ	PROPN
ejpam-6985	293	37	,	,	PUNCT
ejpam-6985	293	38	ϕλ	ϕλ	PROPN
ejpam-6985	293	39	)	)	PUNCT
ejpam-6985	293	40	,	,	PUNCT
ejpam-6985	293	41	∥ϕλ∥l2(µ	∥ϕλ∥l2(µ	PROPN
ejpam-6985	293	42	)	)	PUNCT
ejpam-6985	293	43	=	=	SYM
ejpam-6985	294	1	1	1	X
ejpam-6985	294	2	.	.	PUNCT
ejpam-6985	294	3	a.	a.	PROPN
ejpam-6985	294	4	ben	ben	PROPN
ejpam-6985	294	5	ahmed	ahmed	PROPN
ejpam-6985	294	6	/	/	SYM
ejpam-6985	294	7	eur	eur	PROPN
ejpam-6985	294	8	.	.	PUNCT
ejpam-6985	295	1	j.	j.	PROPN
ejpam-6985	295	2	pure	pure	PROPN
ejpam-6985	295	3	appl	appl	PROPN
ejpam-6985	295	4	.	.	PROPN
ejpam-6985	295	5	math	math	PROPN
ejpam-6985	295	6	,	,	PUNCT
ejpam-6985	295	7	18	18	NUM
ejpam-6985	295	8	(	(	PUNCT
ejpam-6985	295	9	4	4	NUM
ejpam-6985	295	10	)	)	PUNCT
ejpam-6985	295	11	(	(	PUNCT
ejpam-6985	295	12	2025	2025	NUM
ejpam-6985	295	13	)	)	PUNCT
ejpam-6985	295	14	,	,	PUNCT
ejpam-6985	295	15	6985	6985	NUM
ejpam-6985	295	16	14	14	NUM
ejpam-6985	295	17	of	of	ADP
ejpam-6985	295	18	16	16	NUM
ejpam-6985	295	19	differentiate	differentiate	NOUN
ejpam-6985	295	20	at	at	ADP
ejpam-6985	295	21	λ	λ	X
ejpam-6985	295	22	=	=	NOUN
ejpam-6985	295	23	0	0	NUM
ejpam-6985	295	24	:	:	PUNCT
ejpam-6985	295	25	λ̇1(0	λ̇1(0	PROPN
ejpam-6985	295	26	)	)	PUNCT
ejpam-6985	295	27	=	=	SYM
ejpam-6985	295	28	ȧ0(ϕ0	ȧ0(ϕ0	NOUN
ejpam-6985	295	29	,	,	PUNCT
ejpam-6985	295	30	ϕ0	ϕ0	NOUN
ejpam-6985	295	31	)	)	PUNCT
ejpam-6985	295	32	+	+	CCONJ
ejpam-6985	295	33	2	2	NUM
ejpam-6985	295	34	a0(ϕ0	a0(ϕ0	NOUN
ejpam-6985	295	35	,	,	PUNCT
ejpam-6985	295	36	ϕ̇0	ϕ̇0	NOUN
ejpam-6985	295	37	)	)	PUNCT
ejpam-6985	295	38	.	.	PUNCT
ejpam-6985	296	1	but	but	CCONJ
ejpam-6985	296	2	a0(ϕ0	a0(ϕ0	NOUN
ejpam-6985	296	3	,	,	PUNCT
ejpam-6985	296	4	·	·	PUNCT
ejpam-6985	296	5	)	)	PUNCT
ejpam-6985	296	6	represents	represent	VERB
ejpam-6985	296	7	the	the	DET
ejpam-6985	296	8	bounded	bounded	ADJ
ejpam-6985	296	9	functional	functional	ADJ
ejpam-6985	296	10	v	v	ADP
ejpam-6985	296	11	7→	7→	NUM
ejpam-6985	296	12	⟨∆0	⟨∆0	PROPN
ejpam-6985	296	13	bϕ0	bϕ0	NOUN
ejpam-6985	296	14	,	,	PUNCT
ejpam-6985	296	15	v⟩	v⟩	NOUN
ejpam-6985	296	16	=	=	SYM
ejpam-6985	296	17	λ1(0)⟨ϕ0	λ1(0)⟨ϕ0	NOUN
ejpam-6985	296	18	,	,	PUNCT
ejpam-6985	296	19	v⟩	v⟩	NOUN
ejpam-6985	296	20	,	,	PUNCT
ejpam-6985	296	21	hence	hence	ADV
ejpam-6985	296	22	a0(ϕ0	a0(ϕ0	PRON
ejpam-6985	296	23	,	,	PUNCT
ejpam-6985	296	24	ϕ̇0	ϕ̇0	NOUN
ejpam-6985	296	25	)	)	PUNCT
ejpam-6985	297	1	=	=	SYM
ejpam-6985	297	2	λ1(0)⟨ϕ0	λ1(0)⟨ϕ0	NOUN
ejpam-6985	297	3	,	,	PUNCT
ejpam-6985	297	4	ϕ̇0⟩	ϕ̇0⟩	PROPN
ejpam-6985	298	1	=	=	SYM
ejpam-6985	298	2	0	0	NUM
ejpam-6985	298	3	by	by	ADP
ejpam-6985	298	4	(	(	PUNCT
ejpam-6985	298	5	6.7	6.7	NUM
ejpam-6985	298	6	)	)	PUNCT
ejpam-6985	298	7	.	.	PUNCT
ejpam-6985	299	1	therefore	therefore	ADV
ejpam-6985	299	2	λ̇1(0	λ̇1(0	PROPN
ejpam-6985	299	3	)	)	PUNCT
ejpam-6985	299	4	=	=	SYM
ejpam-6985	299	5	ȧ0(ϕ0	ȧ0(ϕ0	NOUN
ejpam-6985	299	6	,	,	PUNCT
ejpam-6985	299	7	ϕ0	ϕ0	NOUN
ejpam-6985	299	8	)	)	PUNCT
ejpam-6985	299	9	.	.	PUNCT
ejpam-6985	300	1	since	since	SCONJ
ejpam-6985	300	2	ȧ0(ϕ0	ȧ0(ϕ0	NOUN
ejpam-6985	300	3	,	,	PUNCT
ejpam-6985	300	4	ϕ0	ϕ0	NOUN
ejpam-6985	300	5	)	)	PUNCT
ejpam-6985	300	6	=	=	PUNCT
ejpam-6985	301	1	⟨∆̇0	⟨∆̇0	NOUN
ejpam-6985	301	2	bϕ0	bϕ0	NOUN
ejpam-6985	301	3	,	,	PUNCT
ejpam-6985	301	4	ϕ0⟩	ϕ0⟩	PRON
ejpam-6985	301	5	,	,	PUNCT
ejpam-6985	301	6	we	we	PRON
ejpam-6985	301	7	recover	recover	VERB
ejpam-6985	301	8	(	(	PUNCT
ejpam-6985	301	9	6.4	6.4	NUM
ejpam-6985	301	10	)	)	PUNCT
ejpam-6985	301	11	.	.	PUNCT
ejpam-6985	302	1	step	step	NOUN
ejpam-6985	302	2	5	5	NUM
ejpam-6985	302	3	:	:	PUNCT
ejpam-6985	302	4	on	on	ADP
ejpam-6985	302	5	the	the	DET
ejpam-6985	302	6	operator	operator	NOUN
ejpam-6985	302	7	derivative	derivative	NOUN
ejpam-6985	302	8	∆̇0	∆̇0	PROPN
ejpam-6985	302	9	b	b	PROPN
ejpam-6985	302	10	in	in	ADP
ejpam-6985	302	11	the	the	DET
ejpam-6985	302	12	cr	cr	NOUN
ejpam-6985	302	13	setting	set	VERB
ejpam-6985	302	14	.	.	PUNCT
ejpam-6985	303	1	in	in	ADP
ejpam-6985	303	2	pseudo	pseudo	NOUN
ejpam-6985	303	3	-	-	ADJ
ejpam-6985	303	4	hermitian	hermitian	ADJ
ejpam-6985	303	5	geometry	geometry	NOUN
ejpam-6985	303	6	one	one	NOUN
ejpam-6985	303	7	typically	typically	ADV
ejpam-6985	303	8	writes	write	VERB
ejpam-6985	303	9	∆λ	∆λ	PROPN
ejpam-6985	303	10	b	b	PROPN
ejpam-6985	303	11	=	=	NOUN
ejpam-6985	303	12	−divλµ(∇λ	−divλµ(∇λ	X
ejpam-6985	303	13	b	b	PROPN
ejpam-6985	303	14	)	)	PUNCT
ejpam-6985	303	15	in	in	ADP
ejpam-6985	303	16	terms	term	NOUN
ejpam-6985	303	17	of	of	ADP
ejpam-6985	303	18	the	the	DET
ejpam-6985	303	19	λ	λ	NOUN
ejpam-6985	303	20	-	-	ADJ
ejpam-6985	303	21	dependent	dependent	ADJ
ejpam-6985	303	22	horizontal	horizontal	ADJ
ejpam-6985	303	23	gradient	gradient	NOUN
ejpam-6985	303	24	and	and	CCONJ
ejpam-6985	303	25	divergence	divergence	NOUN
ejpam-6985	303	26	,	,	PUNCT
ejpam-6985	303	27	the	the	DET
ejpam-6985	303	28	former	former	ADJ
ejpam-6985	303	29	depending	depend	VERB
ejpam-6985	303	30	on	on	ADP
ejpam-6985	303	31	(	(	PUNCT
ejpam-6985	303	32	θλ	θλ	NOUN
ejpam-6985	303	33	,	,	PUNCT
ejpam-6985	303	34	jλ	jλ	NOUN
ejpam-6985	303	35	)	)	PUNCT
ejpam-6985	303	36	and	and	CCONJ
ejpam-6985	303	37	the	the	DET
ejpam-6985	303	38	levi	levi	PROPN
ejpam-6985	303	39	form	form	NOUN
ejpam-6985	303	40	,	,	PUNCT
ejpam-6985	303	41	the	the	DET
ejpam-6985	303	42	latter	latter	ADJ
ejpam-6985	303	43	on	on	ADP
ejpam-6985	303	44	the	the	DET
ejpam-6985	303	45	fixed	fix	VERB
ejpam-6985	303	46	measure	measure	NOUN
ejpam-6985	303	47	µ	µ	X
ejpam-6985	303	48	(	(	PUNCT
ejpam-6985	303	49	or	or	CCONJ
ejpam-6985	303	50	,	,	PUNCT
ejpam-6985	303	51	if	if	SCONJ
ejpam-6985	303	52	the	the	DET
ejpam-6985	303	53	geometric	geometric	ADJ
ejpam-6985	303	54	volume	volume	NOUN
ejpam-6985	303	55	µλ	µλ	NOUN
ejpam-6985	303	56	is	be	AUX
ejpam-6985	303	57	preferred	prefer	VERB
ejpam-6985	303	58	,	,	PUNCT
ejpam-6985	303	59	one	one	NUM
ejpam-6985	303	60	transports	transport	NOUN
ejpam-6985	303	61	to	to	ADP
ejpam-6985	303	62	the	the	DET
ejpam-6985	303	63	fixed	fix	VERB
ejpam-6985	303	64	hilbert	hilbert	NOUN
ejpam-6985	303	65	space	space	NOUN
ejpam-6985	303	66	via	via	ADP
ejpam-6985	303	67	the	the	DET
ejpam-6985	303	68	unitary	unitary	ADJ
ejpam-6985	303	69	uλf	uλf	NOUN
ejpam-6985	303	70	:	:	PUNCT
ejpam-6985	303	71	=	=	SYM
ejpam-6985	303	72	(	(	PUNCT
ejpam-6985	303	73	dµλ	dµλ	INTJ
ejpam-6985	303	74	dµ	dµ	ADJ
ejpam-6985	303	75	)	)	PUNCT
ejpam-6985	303	76	1/2	1/2	NUM
ejpam-6985	303	77	f	f	NOUN
ejpam-6985	303	78	;	;	PUNCT
ejpam-6985	303	79	this	this	PRON
ejpam-6985	303	80	falls	fall	VERB
ejpam-6985	303	81	under	under	ADP
ejpam-6985	303	82	kato	kato	PROPN
ejpam-6985	303	83	’s	’s	PART
ejpam-6985	303	84	unitary	unitary	ADJ
ejpam-6985	303	85	equivalence	equivalence	NOUN
ejpam-6985	303	86	)	)	PUNCT
ejpam-6985	303	87	.	.	PUNCT
ejpam-6985	304	1	differentiating	differentiate	VERB
ejpam-6985	304	2	at	at	ADP
ejpam-6985	304	3	λ	λ	X
ejpam-6985	304	4	=	=	SYM
ejpam-6985	304	5	0	0	NUM
ejpam-6985	304	6	gives	give	VERB
ejpam-6985	304	7	a	a	DET
ejpam-6985	304	8	symmetric	symmetric	ADJ
ejpam-6985	304	9	first	first	ADJ
ejpam-6985	304	10	-	-	PUNCT
ejpam-6985	304	11	order	order	NOUN
ejpam-6985	304	12	differential	differential	NOUN
ejpam-6985	304	13	operator	operator	NOUN
ejpam-6985	304	14	∆̇0	∆̇0	PROPN
ejpam-6985	304	15	b	b	NOUN
ejpam-6985	304	16	whose	whose	DET
ejpam-6985	304	17	coefficients	coefficient	NOUN
ejpam-6985	304	18	are	be	AUX
ejpam-6985	304	19	affine	affine	NOUN
ejpam-6985	304	20	in	in	ADP
ejpam-6985	304	21	the	the	DET
ejpam-6985	304	22	variations	variation	NOUN
ejpam-6985	304	23	θ̇	θ̇	ADP
ejpam-6985	304	24	,	,	PUNCT
ejpam-6985	304	25	j̇	j̇	NOUN
ejpam-6985	304	26	and	and	CCONJ
ejpam-6985	304	27	in	in	ADP
ejpam-6985	304	28	the	the	DET
ejpam-6985	304	29	variation	variation	NOUN
ejpam-6985	304	30	of	of	ADP
ejpam-6985	304	31	the	the	DET
ejpam-6985	304	32	levi	levi	PROPN
ejpam-6985	304	33	form	form	PROPN
ejpam-6985	304	34	/	/	SYM
ejpam-6985	304	35	webster	webster	PROPN
ejpam-6985	304	36	metric	metric	PROPN
ejpam-6985	304	37	;	;	PUNCT
ejpam-6985	304	38	the	the	DET
ejpam-6985	304	39	formula	formula	NOUN
ejpam-6985	304	40	(	(	PUNCT
ejpam-6985	304	41	6.4	6.4	NUM
ejpam-6985	304	42	)	)	PUNCT
ejpam-6985	304	43	then	then	ADV
ejpam-6985	304	44	evaluates	evaluate	VERB
ejpam-6985	304	45	λ̇1(0	λ̇1(0	PRON
ejpam-6985	304	46	)	)	PUNCT
ejpam-6985	304	47	as	as	ADP
ejpam-6985	304	48	the	the	DET
ejpam-6985	304	49	expectation	expectation	NOUN
ejpam-6985	304	50	of	of	ADP
ejpam-6985	304	51	this	this	DET
ejpam-6985	304	52	operator	operator	NOUN
ejpam-6985	304	53	in	in	ADP
ejpam-6985	304	54	the	the	DET
ejpam-6985	304	55	ground	ground	NOUN
ejpam-6985	304	56	state	state	PROPN
ejpam-6985	304	57	ϕ0	ϕ0	PROPN
ejpam-6985	304	58	.	.	PUNCT
ejpam-6985	305	1	remark	remark	NOUN
ejpam-6985	305	2	4	4	NUM
ejpam-6985	305	3	(	(	PUNCT
ejpam-6985	305	4	on	on	ADP
ejpam-6985	305	5	domains	domain	NOUN
ejpam-6985	305	6	and	and	CCONJ
ejpam-6985	305	7	regularity	regularity	NOUN
ejpam-6985	305	8	)	)	PUNCT
ejpam-6985	305	9	.	.	PUNCT
ejpam-6985	306	1	assumption	assumption	NOUN
ejpam-6985	306	2	(	(	PUNCT
ejpam-6985	306	3	ii	ii	NOUN
ejpam-6985	306	4	)	)	PUNCT
ejpam-6985	306	5	is	be	AUX
ejpam-6985	306	6	satisfied	satisfied	ADJ
ejpam-6985	306	7	in	in	ADP
ejpam-6985	306	8	two	two	NUM
ejpam-6985	306	9	standard	standard	ADJ
ejpam-6985	306	10	setups	setup	NOUN
ejpam-6985	306	11	:	:	PUNCT
ejpam-6985	306	12	(	(	PUNCT
ejpam-6985	306	13	a	a	X
ejpam-6985	306	14	)	)	PUNCT
ejpam-6985	306	15	operator	operator	NOUN
ejpam-6985	306	16	sense	sense	NOUN
ejpam-6985	306	17	:	:	PUNCT
ejpam-6985	306	18	there	there	PRON
ejpam-6985	306	19	exists	exist	VERB
ejpam-6985	306	20	a	a	DET
ejpam-6985	306	21	common	common	ADJ
ejpam-6985	306	22	core	core	NOUN
ejpam-6985	306	23	d	d	PROPN
ejpam-6985	306	24	⊂	⊂	PROPN
ejpam-6985	306	25	w	w	PROPN
ejpam-6985	306	26	2,2	2,2	NUM
ejpam-6985	306	27	h	h	PROPN
ejpam-6985	306	28	(	(	PUNCT
ejpam-6985	306	29	m	m	NOUN
ejpam-6985	306	30	)	)	PUNCT
ejpam-6985	306	31	such	such	ADJ
ejpam-6985	306	32	that	that	SCONJ
ejpam-6985	306	33	∆λ	∆λ	PROPN
ejpam-6985	306	34	b	b	PROPN
ejpam-6985	306	35	|d	|d	NOUN
ejpam-6985	306	36	depends	depend	VERB
ejpam-6985	306	37	c1	c1	PROPN
ejpam-6985	306	38	on	on	ADP
ejpam-6985	306	39	λ	λ	PROPN
ejpam-6985	306	40	in	in	ADP
ejpam-6985	306	41	the	the	DET
ejpam-6985	306	42	graph	graph	NOUN
ejpam-6985	306	43	norm	norm	NOUN
ejpam-6985	306	44	;	;	PUNCT
ejpam-6985	306	45	or	or	CCONJ
ejpam-6985	306	46	(	(	PUNCT
ejpam-6985	306	47	b	b	NOUN
ejpam-6985	306	48	)	)	PUNCT
ejpam-6985	306	49	form	form	NOUN
ejpam-6985	306	50	sense	sense	NOUN
ejpam-6985	306	51	:	:	PUNCT
ejpam-6985	306	52	each	each	DET
ejpam-6985	306	53	∆λ	∆λ	PROPN
ejpam-6985	306	54	b	b	PROPN
ejpam-6985	306	55	is	be	AUX
ejpam-6985	306	56	associated	associate	VERB
ejpam-6985	306	57	with	with	ADP
ejpam-6985	306	58	a	a	DET
ejpam-6985	306	59	closed	closed	ADJ
ejpam-6985	306	60	coercive	coercive	ADJ
ejpam-6985	306	61	form	form	NOUN
ejpam-6985	306	62	aλ	aλ	ADP
ejpam-6985	306	63	on	on	ADP
ejpam-6985	306	64	the	the	DET
ejpam-6985	306	65	common	common	ADJ
ejpam-6985	306	66	form	form	NOUN
ejpam-6985	306	67	domain	domain	NOUN
ejpam-6985	306	68	v	v	ADP
ejpam-6985	306	69	=	=	PROPN
ejpam-6985	306	70	w	w	PROPN
ejpam-6985	306	71	1,2	1,2	NUM
ejpam-6985	306	72	h	h	NOUN
ejpam-6985	306	73	(	(	PUNCT
ejpam-6985	306	74	m	m	NOUN
ejpam-6985	306	75	)	)	PUNCT
ejpam-6985	306	76	and	and	CCONJ
ejpam-6985	307	1	λ	λ	X
ejpam-6985	307	2	7→	7→	PROPN
ejpam-6985	307	3	aλ	aλ	ADP
ejpam-6985	307	4	is	be	AUX
ejpam-6985	307	5	c1	c1	PROPN
ejpam-6985	307	6	.	.	PUNCT
ejpam-6985	308	1	in	in	ADP
ejpam-6985	308	2	case	case	NOUN
ejpam-6985	308	3	(	(	PUNCT
ejpam-6985	308	4	b	b	X
ejpam-6985	308	5	)	)	PUNCT
ejpam-6985	308	6	the	the	DET
ejpam-6985	308	7	above	above	ADJ
ejpam-6985	308	8	proof	proof	NOUN
ejpam-6985	308	9	via	via	ADP
ejpam-6985	308	10	forms	form	NOUN
ejpam-6985	308	11	applies	apply	VERB
ejpam-6985	308	12	verbatim	verbatim	ADJ
ejpam-6985	308	13	and	and	CCONJ
ejpam-6985	308	14	is	be	AUX
ejpam-6985	308	15	often	often	ADV
ejpam-6985	308	16	technically	technically	ADV
ejpam-6985	308	17	simpler	simple	ADJ
ejpam-6985	308	18	in	in	ADP
ejpam-6985	308	19	cr	cr	X
ejpam-6985	308	20	geometry	geometry	NOUN
ejpam-6985	308	21	where	where	SCONJ
ejpam-6985	308	22	coefficients	coefficient	NOUN
ejpam-6985	308	23	appear	appear	VERB
ejpam-6985	308	24	in	in	ADP
ejpam-6985	308	25	divergence	divergence	NOUN
ejpam-6985	308	26	form	form	NOUN
ejpam-6985	308	27	.	.	PUNCT
ejpam-6985	309	1	see	see	VERB
ejpam-6985	309	2	[	[	X
ejpam-6985	309	3	17	17	NUM
ejpam-6985	309	4	,	,	PUNCT
ejpam-6985	309	5	ch	ch	NOUN
ejpam-6985	309	6	.	.	PROPN
ejpam-6985	309	7	vi	vi	PROPN
ejpam-6985	309	8	–	–	PUNCT
ejpam-6985	309	9	vii	vii	NOUN
ejpam-6985	309	10	]	]	PUNCT
ejpam-6985	309	11	.	.	PUNCT
ejpam-6985	310	1	remark	remark	PROPN
ejpam-6985	310	2	5	5	NUM
ejpam-6985	310	3	(	(	PUNCT
ejpam-6985	310	4	role	role	NOUN
ejpam-6985	310	5	of	of	ADP
ejpam-6985	310	6	torsion	torsion	NOUN
ejpam-6985	310	7	)	)	PUNCT
ejpam-6985	310	8	.	.	PUNCT
ejpam-6985	311	1	the	the	DET
ejpam-6985	311	2	formula	formula	NOUN
ejpam-6985	311	3	(	(	PUNCT
ejpam-6985	311	4	6.4	6.4	NUM
ejpam-6985	311	5	)	)	PUNCT
ejpam-6985	311	6	is	be	AUX
ejpam-6985	311	7	purely	purely	ADV
ejpam-6985	311	8	spectral	spectral	ADJ
ejpam-6985	311	9	/	/	SYM
ejpam-6985	311	10	variational	variational	ADJ
ejpam-6985	311	11	and	and	CCONJ
ejpam-6985	311	12	holds	hold	VERB
ejpam-6985	311	13	regardless	regardless	ADV
ejpam-6985	311	14	of	of	ADP
ejpam-6985	311	15	torsion	torsion	NOUN
ejpam-6985	311	16	;	;	PUNCT
ejpam-6985	311	17	torsion	torsion	NOUN
ejpam-6985	311	18	enters	enter	VERB
ejpam-6985	311	19	through	through	ADP
ejpam-6985	311	20	the	the	DET
ejpam-6985	311	21	explicit	explicit	ADJ
ejpam-6985	311	22	expression	expression	NOUN
ejpam-6985	311	23	of	of	ADP
ejpam-6985	311	24	∆̇0	∆̇0	PROPN
ejpam-6985	311	25	b	b	PROPN
ejpam-6985	311	26	in	in	ADP
ejpam-6985	311	27	terms	term	NOUN
ejpam-6985	311	28	of	of	ADP
ejpam-6985	311	29	the	the	DET
ejpam-6985	311	30	tanaka	tanaka	PROPN
ejpam-6985	311	31	–	–	PUNCT
ejpam-6985	311	32	webster	webster	PROPN
ejpam-6985	311	33	connection	connection	NOUN
ejpam-6985	311	34	.	.	PUNCT
ejpam-6985	312	1	in	in	ADP
ejpam-6985	312	2	sasakian	sasakian	PROPN
ejpam-6985	312	3	(	(	PUNCT
ejpam-6985	312	4	torsion	torsion	NOUN
ejpam-6985	312	5	-	-	PUNCT
ejpam-6985	312	6	free	free	ADJ
ejpam-6985	312	7	)	)	PUNCT
ejpam-6985	312	8	deformations	deformation	NOUN
ejpam-6985	312	9	,	,	PUNCT
ejpam-6985	312	10	the	the	DET
ejpam-6985	312	11	same	same	ADJ
ejpam-6985	312	12	identity	identity	NOUN
ejpam-6985	312	13	holds	hold	VERB
ejpam-6985	312	14	with	with	ADP
ejpam-6985	312	15	a	a	DET
ejpam-6985	312	16	simpler	simple	ADJ
ejpam-6985	312	17	∆̇0	∆̇0	PROPN
ejpam-6985	312	18	b	b	PROPN
ejpam-6985	312	19	(	(	PUNCT
ejpam-6985	312	20	no	no	DET
ejpam-6985	312	21	first	first	ADJ
ejpam-6985	312	22	-	-	PUNCT
ejpam-6985	312	23	order	order	NOUN
ejpam-6985	312	24	torsion	torsion	NOUN
ejpam-6985	312	25	terms	term	NOUN
ejpam-6985	312	26	)	)	PUNCT
ejpam-6985	312	27	.	.	PUNCT
ejpam-6985	313	1	in	in	ADP
ejpam-6985	313	2	general	general	ADJ
ejpam-6985	313	3	pseudo	pseudo	NOUN
ejpam-6985	313	4	-	-	ADJ
ejpam-6985	313	5	hermitian	hermitian	ADJ
ejpam-6985	313	6	deformations	deformation	NOUN
ejpam-6985	313	7	,	,	PUNCT
ejpam-6985	313	8	the	the	DET
ejpam-6985	313	9	torsion	torsion	NOUN
ejpam-6985	313	10	variation	variation	NOUN
ejpam-6985	313	11	contributes	contribute	VERB
ejpam-6985	313	12	linear	linear	ADJ
ejpam-6985	313	13	terms	term	NOUN
ejpam-6985	313	14	to	to	ADP
ejpam-6985	313	15	∆̇0	∆̇0	PROPN
ejpam-6985	313	16	b	b	PROPN
ejpam-6985	313	17	but	but	CCONJ
ejpam-6985	313	18	the	the	DET
ejpam-6985	313	19	hellmann	hellmann	PROPN
ejpam-6985	313	20	–	–	PUNCT
ejpam-6985	313	21	feynman	feynman	PROPN
ejpam-6985	313	22	identity	identity	NOUN
ejpam-6985	313	23	remains	remain	VERB
ejpam-6985	313	24	unchanged	unchanged	ADJ
ejpam-6985	313	25	.	.	PUNCT
ejpam-6985	314	1	7	7	X
ejpam-6985	314	2	.	.	X
ejpam-6985	314	3	conclusion	conclusion	NOUN
ejpam-6985	314	4	in	in	ADP
ejpam-6985	314	5	this	this	DET
ejpam-6985	314	6	work	work	NOUN
ejpam-6985	314	7	,	,	PUNCT
ejpam-6985	314	8	we	we	PRON
ejpam-6985	314	9	established	establish	VERB
ejpam-6985	314	10	cheeger	cheeger	ADV
ejpam-6985	314	11	and	and	CCONJ
ejpam-6985	314	12	buser	buser	NOUN
ejpam-6985	314	13	–	–	PUNCT
ejpam-6985	314	14	type	type	NOUN
ejpam-6985	314	15	inequalities	inequality	NOUN
ejpam-6985	314	16	for	for	ADP
ejpam-6985	314	17	the	the	DET
ejpam-6985	314	18	first	first	ADJ
ejpam-6985	314	19	positive	positive	ADJ
ejpam-6985	314	20	eigenvalue	eigenvalue	NOUN
ejpam-6985	314	21	of	of	ADP
ejpam-6985	314	22	the	the	DET
ejpam-6985	314	23	sub	sub	NOUN
ejpam-6985	314	24	-	-	NOUN
ejpam-6985	314	25	laplacian	laplacian	ADJ
ejpam-6985	314	26	on	on	ADP
ejpam-6985	314	27	compact	compact	ADJ
ejpam-6985	314	28	strictly	strictly	ADV
ejpam-6985	314	29	pseudoconvex	pseudoconvex	VERB
ejpam-6985	314	30	pseudo	pseudo	NOUN
ejpam-6985	314	31	-	-	ADJ
ejpam-6985	314	32	hermitian	hermitian	ADJ
ejpam-6985	314	33	cr	cr	PROPN
ejpam-6985	314	34	manifolds	manifolds	PROPN
ejpam-6985	314	35	.	.	PUNCT
ejpam-6985	315	1	these	these	DET
ejpam-6985	315	2	inequalities	inequality	NOUN
ejpam-6985	315	3	connect	connect	VERB
ejpam-6985	315	4	the	the	DET
ejpam-6985	315	5	spectral	spectral	ADJ
ejpam-6985	315	6	gap	gap	NOUN
ejpam-6985	315	7	to	to	ADP
ejpam-6985	315	8	a	a	DET
ejpam-6985	315	9	geometric	geometric	ADJ
ejpam-6985	315	10	invariant	invariant	NOUN
ejpam-6985	315	11	,	,	PUNCT
ejpam-6985	315	12	the	the	DET
ejpam-6985	315	13	cr	cr	NOUN
ejpam-6985	315	14	cheeger	cheeger	ADV
ejpam-6985	315	15	constant	constant	ADJ
ejpam-6985	315	16	,	,	PUNCT
ejpam-6985	315	17	thereby	thereby	ADV
ejpam-6985	315	18	extending	extend	VERB
ejpam-6985	315	19	classical	classical	ADJ
ejpam-6985	315	20	riemannian	riemannian	ADJ
ejpam-6985	315	21	isoperimetric	isoperimetric	NOUN
ejpam-6985	315	22	theory	theory	NOUN
ejpam-6985	315	23	to	to	ADP
ejpam-6985	315	24	the	the	DET
ejpam-6985	315	25	cr	cr	PROPN
ejpam-6985	315	26	framework	framework	PROPN
ejpam-6985	315	27	.	.	PUNCT
ejpam-6985	316	1	our	our	PRON
ejpam-6985	316	2	approach	approach	NOUN
ejpam-6985	316	3	combines	combine	VERB
ejpam-6985	316	4	horizontal	horizontal	ADJ
ejpam-6985	316	5	bv	bv	PROPN
ejpam-6985	316	6	methods	method	NOUN
ejpam-6985	316	7	,	,	PUNCT
ejpam-6985	316	8	the	the	DET
ejpam-6985	316	9	co	co	NOUN
ejpam-6985	316	10	-	-	NOUN
ejpam-6985	316	11	area	area	NOUN
ejpam-6985	316	12	formula	formula	NOUN
ejpam-6985	316	13	,	,	PUNCT
ejpam-6985	316	14	and	and	CCONJ
ejpam-6985	316	15	poincaré	poincaré	ADJ
ejpam-6985	316	16	inequalities	inequality	NOUN
ejpam-6985	316	17	within	within	ADP
ejpam-6985	316	18	a	a	DET
ejpam-6985	316	19	unified	unified	ADJ
ejpam-6985	316	20	sub	sub	ADJ
ejpam-6985	316	21	-	-	ADJ
ejpam-6985	316	22	riemannian	riemannian	ADJ
ejpam-6985	316	23	analytic	analytic	ADJ
ejpam-6985	316	24	setting	setting	NOUN
ejpam-6985	316	25	.	.	PUNCT
ejpam-6985	317	1	this	this	PRON
ejpam-6985	317	2	provides	provide	VERB
ejpam-6985	317	3	new	new	ADJ
ejpam-6985	317	4	insight	insight	NOUN
ejpam-6985	317	5	into	into	ADP
ejpam-6985	317	6	the	the	DET
ejpam-6985	317	7	interplay	interplay	NOUN
ejpam-6985	317	8	between	between	ADP
ejpam-6985	317	9	geometry	geometry	NOUN
ejpam-6985	317	10	,	,	PUNCT
ejpam-6985	317	11	torsion	torsion	NOUN
ejpam-6985	317	12	,	,	PUNCT
ejpam-6985	317	13	and	and	CCONJ
ejpam-6985	317	14	spectral	spectral	ADJ
ejpam-6985	317	15	properties	property	NOUN
ejpam-6985	317	16	in	in	ADP
ejpam-6985	317	17	pseudohermitian	pseudohermitian	ADJ
ejpam-6985	317	18	manifolds	manifold	NOUN
ejpam-6985	317	19	.	.	PUNCT
ejpam-6985	318	1	the	the	DET
ejpam-6985	318	2	analysis	analysis	NOUN
ejpam-6985	318	3	also	also	ADV
ejpam-6985	318	4	highlights	highlight	VERB
ejpam-6985	318	5	how	how	SCONJ
ejpam-6985	318	6	curvature	curvature	NOUN
ejpam-6985	318	7	and	and	CCONJ
ejpam-6985	318	8	torsion	torsion	NOUN
ejpam-6985	318	9	quantitatively	quantitatively	ADV
ejpam-6985	318	10	influence	influence	VERB
ejpam-6985	318	11	the	the	DET
ejpam-6985	318	12	constants	constant	NOUN
ejpam-6985	318	13	appearing	appear	VERB
ejpam-6985	318	14	in	in	ADP
ejpam-6985	318	15	isoperimetric	isoperimetric	ADJ
ejpam-6985	318	16	and	and	CCONJ
ejpam-6985	318	17	spectral	spectral	ADJ
ejpam-6985	318	18	inequalities	inequality	NOUN
ejpam-6985	318	19	.	.	PUNCT
ejpam-6985	319	1	future	future	ADJ
ejpam-6985	319	2	work	work	NOUN
ejpam-6985	319	3	a.	a.	PROPN
ejpam-6985	319	4	ben	ben	PROPN
ejpam-6985	319	5	ahmed	ahmed	PROPN
ejpam-6985	319	6	/	/	SYM
ejpam-6985	319	7	eur	eur	PROPN
ejpam-6985	319	8	.	.	PUNCT
ejpam-6985	320	1	j.	j.	PROPN
ejpam-6985	320	2	pure	pure	PROPN
ejpam-6985	320	3	appl	appl	PROPN
ejpam-6985	320	4	.	.	PROPN
ejpam-6985	320	5	math	math	PROPN
ejpam-6985	320	6	,	,	PUNCT
ejpam-6985	320	7	18	18	NUM
ejpam-6985	320	8	(	(	PUNCT
ejpam-6985	320	9	4	4	NUM
ejpam-6985	320	10	)	)	PUNCT
ejpam-6985	320	11	(	(	PUNCT
ejpam-6985	320	12	2025	2025	NUM
ejpam-6985	320	13	)	)	PUNCT
ejpam-6985	320	14	,	,	PUNCT
ejpam-6985	320	15	6985	6985	NUM
ejpam-6985	320	16	15	15	NUM
ejpam-6985	320	17	of	of	ADP
ejpam-6985	320	18	16	16	NUM
ejpam-6985	320	19	will	will	AUX
ejpam-6985	320	20	focus	focus	VERB
ejpam-6985	320	21	on	on	ADP
ejpam-6985	320	22	boundary	boundary	ADJ
ejpam-6985	320	23	analogues	analogue	NOUN
ejpam-6985	320	24	,	,	PUNCT
ejpam-6985	320	25	higher	high	ADJ
ejpam-6985	320	26	eigenvalues	eigenvalue	NOUN
ejpam-6985	320	27	,	,	PUNCT
ejpam-6985	320	28	and	and	CCONJ
ejpam-6985	320	29	the	the	DET
ejpam-6985	320	30	stability	stability	NOUN
ejpam-6985	320	31	of	of	ADP
ejpam-6985	320	32	the	the	DET
ejpam-6985	320	33	spectral	spectral	ADJ
ejpam-6985	320	34	gap	gap	NOUN
ejpam-6985	320	35	under	under	ADP
ejpam-6985	320	36	cr	cr	NOUN
ejpam-6985	320	37	deformations	deformation	NOUN
ejpam-6985	320	38	.	.	PUNCT
ejpam-6985	321	1	acknowledgements	acknowledgement	NOUN
ejpam-6985	321	2	the	the	DET
ejpam-6985	321	3	author	author	NOUN
ejpam-6985	321	4	expresses	express	VERB
ejpam-6985	321	5	his	his	PRON
ejpam-6985	321	6	sincere	sincere	ADJ
ejpam-6985	321	7	appreciation	appreciation	NOUN
ejpam-6985	321	8	to	to	ADP
ejpam-6985	321	9	the	the	DET
ejpam-6985	321	10	reviewers	reviewer	NOUN
ejpam-6985	321	11	for	for	ADP
ejpam-6985	321	12	their	their	PRON
ejpam-6985	321	13	thorough	thorough	ADJ
ejpam-6985	321	14	evaluation	evaluation	NOUN
ejpam-6985	321	15	of	of	ADP
ejpam-6985	321	16	the	the	DET
ejpam-6985	321	17	manuscript	manuscript	NOUN
ejpam-6985	321	18	and	and	CCONJ
ejpam-6985	321	19	for	for	ADP
ejpam-6985	321	20	their	their	PRON
ejpam-6985	321	21	valuable	valuable	ADJ
ejpam-6985	321	22	comments	comment	NOUN
ejpam-6985	321	23	and	and	CCONJ
ejpam-6985	321	24	constructive	constructive	ADJ
ejpam-6985	321	25	suggestions	suggestion	NOUN
ejpam-6985	321	26	,	,	PUNCT
ejpam-6985	321	27	which	which	PRON
ejpam-6985	321	28	have	have	AUX
ejpam-6985	321	29	helped	help	VERB
ejpam-6985	321	30	to	to	PART
ejpam-6985	321	31	improve	improve	VERB
ejpam-6985	321	32	the	the	DET
ejpam-6985	321	33	clarity	clarity	NOUN
ejpam-6985	321	34	and	and	CCONJ
ejpam-6985	321	35	accuracy	accuracy	NOUN
ejpam-6985	321	36	of	of	ADP
ejpam-6985	321	37	this	this	DET
ejpam-6985	321	38	work	work	NOUN
ejpam-6985	321	39	.	.	PUNCT
ejpam-6985	322	1	references	reference	NOUN
ejpam-6985	322	2	[	[	X
ejpam-6985	322	3	1	1	X
ejpam-6985	322	4	]	]	PUNCT
ejpam-6985	322	5	j.	j.	PROPN
ejpam-6985	322	6	cheeger	cheeger	PROPN
ejpam-6985	322	7	.	.	PUNCT
ejpam-6985	323	1	a	a	DET
ejpam-6985	323	2	lower	lower	ADV
ejpam-6985	323	3	bound	bind	VERB
ejpam-6985	323	4	for	for	ADP
ejpam-6985	323	5	the	the	DET
ejpam-6985	323	6	smallest	small	ADJ
ejpam-6985	323	7	eigenvalue	eigenvalue	NOUN
ejpam-6985	323	8	of	of	ADP
ejpam-6985	323	9	the	the	DET
ejpam-6985	323	10	laplacian	laplacian	NOUN
ejpam-6985	323	11	.	.	PUNCT
ejpam-6985	324	1	in	in	ADP
ejpam-6985	324	2	r.	r.	PROPN
ejpam-6985	324	3	gunning	gunning	PROPN
ejpam-6985	324	4	,	,	PUNCT
ejpam-6985	324	5	editor	editor	NOUN
ejpam-6985	324	6	,	,	PUNCT
ejpam-6985	324	7	problems	problem	NOUN
ejpam-6985	324	8	in	in	ADP
ejpam-6985	324	9	analysis	analysis	NOUN
ejpam-6985	324	10	.	.	PUNCT
ejpam-6985	325	1	princeton	princeton	PROPN
ejpam-6985	325	2	univ	univ	PROPN
ejpam-6985	325	3	.	.	PUNCT
ejpam-6985	326	1	press	press	PROPN
ejpam-6985	326	2	,	,	PUNCT
ejpam-6985	326	3	1970	1970	NUM
ejpam-6985	326	4	.	.	PUNCT
ejpam-6985	327	1	[	[	X
ejpam-6985	327	2	2	2	NUM
ejpam-6985	327	3	]	]	PUNCT
ejpam-6985	327	4	p.	p.	NOUN
ejpam-6985	327	5	buser	buser	PROPN
ejpam-6985	327	6	.	.	PUNCT
ejpam-6985	328	1	a	a	DET
ejpam-6985	328	2	note	note	NOUN
ejpam-6985	328	3	on	on	ADP
ejpam-6985	328	4	the	the	DET
ejpam-6985	328	5	isoperimetric	isoperimetric	ADJ
ejpam-6985	328	6	constant	constant	ADJ
ejpam-6985	328	7	.	.	PUNCT
ejpam-6985	329	1	ann	ann	PROPN
ejpam-6985	329	2	.	.	PUNCT
ejpam-6985	330	1	sci	sci	PROPN
ejpam-6985	330	2	.	.	PUNCT
ejpam-6985	331	1	école	école	ADJ
ejpam-6985	331	2	norm	norm	NOUN
ejpam-6985	331	3	.	.	PUNCT
ejpam-6985	332	1	sup	sup	NOUN
ejpam-6985	332	2	.	.	PUNCT
ejpam-6985	333	1	(	(	PUNCT
ejpam-6985	333	2	4	4	NUM
ejpam-6985	333	3	)	)	PUNCT
ejpam-6985	333	4	,	,	PUNCT
ejpam-6985	333	5	15(2):213–230	15(2):213–230	NUM
ejpam-6985	333	6	,	,	PUNCT
ejpam-6985	333	7	1982	1982	NUM
ejpam-6985	333	8	.	.	PUNCT
ejpam-6985	334	1	[	[	X
ejpam-6985	334	2	3	3	X
ejpam-6985	334	3	]	]	X
ejpam-6985	334	4	g.	g.	PROPN
ejpam-6985	334	5	b.	b.	PROPN
ejpam-6985	334	6	folland	folland	PROPN
ejpam-6985	334	7	and	and	CCONJ
ejpam-6985	334	8	e.	e.	PROPN
ejpam-6985	334	9	m.	m.	PROPN
ejpam-6985	334	10	stein	stein	PROPN
ejpam-6985	334	11	.	.	PUNCT
ejpam-6985	335	1	estimates	estimate	NOUN
ejpam-6985	335	2	for	for	ADP
ejpam-6985	335	3	the	the	DET
ejpam-6985	335	4	∂̄b	∂̄b	NOUN
ejpam-6985	335	5	-	-	PUNCT
ejpam-6985	335	6	complex	complex	NOUN
ejpam-6985	335	7	and	and	CCONJ
ejpam-6985	335	8	analysis	analysis	NOUN
ejpam-6985	335	9	on	on	ADP
ejpam-6985	335	10	the	the	DET
ejpam-6985	335	11	heisenberg	heisenberg	PROPN
ejpam-6985	335	12	group	group	NOUN
ejpam-6985	335	13	.	.	PUNCT
ejpam-6985	336	1	comm	comm	NOUN
ejpam-6985	336	2	.	.	PUNCT
ejpam-6985	337	1	pure	pure	ADJ
ejpam-6985	337	2	appl	appl	PROPN
ejpam-6985	337	3	.	.	PUNCT
ejpam-6985	337	4	math	math	PROPN
ejpam-6985	337	5	.	.	PUNCT
ejpam-6985	337	6	,	,	PUNCT
ejpam-6985	338	1	27:429–522	27:429–522	PROPN
ejpam-6985	338	2	,	,	PUNCT
ejpam-6985	338	3	1974	1974	NUM
ejpam-6985	338	4	.	.	PUNCT
ejpam-6985	339	1	[	[	X
ejpam-6985	339	2	4	4	X
ejpam-6985	339	3	]	]	X
ejpam-6985	339	4	d.	d.	PROPN
ejpam-6985	339	5	jerison	jerison	PROPN
ejpam-6985	339	6	and	and	CCONJ
ejpam-6985	339	7	j.	j.	PROPN
ejpam-6985	339	8	m.	m.	PROPN
ejpam-6985	339	9	lee	lee	PROPN
ejpam-6985	339	10	.	.	PUNCT
ejpam-6985	340	1	the	the	DET
ejpam-6985	340	2	yamabe	yamabe	ADJ
ejpam-6985	340	3	problem	problem	NOUN
ejpam-6985	340	4	on	on	ADP
ejpam-6985	340	5	cr	cr	PROPN
ejpam-6985	340	6	manifolds	manifolds	PROPN
ejpam-6985	340	7	.	.	PUNCT
ejpam-6985	341	1	j.	j.	PROPN
ejpam-6985	341	2	differential	differential	PROPN
ejpam-6985	341	3	geom	geom	PROPN
ejpam-6985	341	4	.	.	PROPN
ejpam-6985	341	5	,	,	PUNCT
ejpam-6985	341	6	25:167–197	25:167–197	NUM
ejpam-6985	341	7	,	,	PUNCT
ejpam-6985	341	8	1987	1987	NUM
ejpam-6985	341	9	.	.	PUNCT
ejpam-6985	342	1	[	[	X
ejpam-6985	342	2	5	5	X
ejpam-6985	342	3	]	]	PUNCT
ejpam-6985	342	4	d.	d.	PROPN
ejpam-6985	342	5	jerison	jerison	PROPN
ejpam-6985	342	6	and	and	CCONJ
ejpam-6985	342	7	j.	j.	PROPN
ejpam-6985	342	8	m.	m.	PROPN
ejpam-6985	342	9	lee	lee	PROPN
ejpam-6985	342	10	.	.	PROPN
ejpam-6985	342	11	intrinsic	intrinsic	PROPN
ejpam-6985	342	12	cr	cr	ADP
ejpam-6985	342	13	normal	normal	ADJ
ejpam-6985	342	14	coordinates	coordinate	NOUN
ejpam-6985	342	15	and	and	CCONJ
ejpam-6985	342	16	the	the	DET
ejpam-6985	342	17	cr	cr	PROPN
ejpam-6985	342	18	yamabe	yamabe	PROPN
ejpam-6985	342	19	problem	problem	NOUN
ejpam-6985	342	20	.	.	PUNCT
ejpam-6985	343	1	j.	j.	PROPN
ejpam-6985	343	2	amer	amer	PROPN
ejpam-6985	343	3	.	.	PROPN
ejpam-6985	343	4	math	math	PROPN
ejpam-6985	343	5	.	.	PUNCT
ejpam-6985	344	1	soc	soc	PROPN
ejpam-6985	344	2	.	.	PUNCT
ejpam-6985	344	3	,	,	PUNCT
ejpam-6985	344	4	1:1–41	1:1–41	NUM
ejpam-6985	344	5	,	,	PUNCT
ejpam-6985	344	6	1988	1988	NUM
ejpam-6985	344	7	.	.	PUNCT
ejpam-6985	345	1	[	[	X
ejpam-6985	345	2	6	6	NUM
ejpam-6985	345	3	]	]	PUNCT
ejpam-6985	345	4	b.	b.	PROPN
ejpam-6985	345	5	franchi	franchi	PROPN
ejpam-6985	345	6	,	,	PUNCT
ejpam-6985	345	7	r.	r.	PROPN
ejpam-6985	345	8	serapioni	serapioni	PROPN
ejpam-6985	345	9	,	,	PUNCT
ejpam-6985	345	10	and	and	CCONJ
ejpam-6985	345	11	f.	f.	PROPN
ejpam-6985	345	12	serra	serra	PROPN
ejpam-6985	345	13	cassano	cassano	PROPN
ejpam-6985	345	14	.	.	PUNCT
ejpam-6985	346	1	rectifiability	rectifiability	NOUN
ejpam-6985	346	2	and	and	CCONJ
ejpam-6985	346	3	perimeter	perimeter	NOUN
ejpam-6985	346	4	in	in	ADP
ejpam-6985	346	5	carnot	carnot	NOUN
ejpam-6985	346	6	–	–	PUNCT
ejpam-6985	346	7	carathéodory	carathéodory	NOUN
ejpam-6985	346	8	spaces	space	NOUN
ejpam-6985	346	9	.	.	PUNCT
ejpam-6985	347	1	math	math	NOUN
ejpam-6985	347	2	.	.	PUNCT
ejpam-6985	348	1	ann	ann	PROPN
ejpam-6985	348	2	.	.	PROPN
ejpam-6985	348	3	,	,	PUNCT
ejpam-6985	348	4	321:479–531	321:479–531	NUM
ejpam-6985	348	5	,	,	PUNCT
ejpam-6985	348	6	2001	2001	NUM
ejpam-6985	348	7	.	.	PUNCT
ejpam-6985	349	1	[	[	X
ejpam-6985	349	2	7	7	X
ejpam-6985	349	3	]	]	X
ejpam-6985	349	4	n.	n.	PROPN
ejpam-6985	349	5	garofalo	garofalo	PROPN
ejpam-6985	349	6	and	and	CCONJ
ejpam-6985	349	7	d.-m	d.-m	PROPN
ejpam-6985	349	8	.	.	PUNCT
ejpam-6985	350	1	nhieu	nhieu	PROPN
ejpam-6985	350	2	.	.	PUNCT
ejpam-6985	351	1	isoperimetric	isoperimetric	PROPN
ejpam-6985	351	2	and	and	CCONJ
ejpam-6985	351	3	sobolev	sobolev	NOUN
ejpam-6985	351	4	inequalities	inequality	NOUN
ejpam-6985	351	5	for	for	ADP
ejpam-6985	351	6	carnot	carnot	NOUN
ejpam-6985	351	7	–	–	PUNCT
ejpam-6985	351	8	carathéodory	carathéodory	NOUN
ejpam-6985	351	9	spaces	space	NOUN
ejpam-6985	351	10	and	and	CCONJ
ejpam-6985	351	11	the	the	DET
ejpam-6985	351	12	existence	existence	NOUN
ejpam-6985	351	13	of	of	ADP
ejpam-6985	351	14	minimal	minimal	ADJ
ejpam-6985	351	15	surfaces	surface	NOUN
ejpam-6985	351	16	.	.	PUNCT
ejpam-6985	352	1	comm	comm	NOUN
ejpam-6985	352	2	.	.	PUNCT
ejpam-6985	353	1	pure	pure	ADJ
ejpam-6985	353	2	appl	appl	PROPN
ejpam-6985	353	3	.	.	PUNCT
ejpam-6985	353	4	math	math	PROPN
ejpam-6985	353	5	.	.	PUNCT
ejpam-6985	353	6	,	,	PUNCT
ejpam-6985	353	7	49:1081–1144	49:1081–1144	NUM
ejpam-6985	353	8	,	,	PUNCT
ejpam-6985	353	9	1996	1996	NUM
ejpam-6985	353	10	.	.	PUNCT
ejpam-6985	354	1	[	[	X
ejpam-6985	354	2	8	8	NUM
ejpam-6985	354	3	]	]	X
ejpam-6985	354	4	f.	f.	PROPN
ejpam-6985	354	5	baudoin	baudoin	PROPN
ejpam-6985	354	6	and	and	CCONJ
ejpam-6985	354	7	n.	n.	PROPN
ejpam-6985	354	8	garofalo	garofalo	PROPN
ejpam-6985	354	9	.	.	PUNCT
ejpam-6985	355	1	curvature	curvature	NOUN
ejpam-6985	355	2	-	-	PUNCT
ejpam-6985	355	3	dimension	dimension	NOUN
ejpam-6985	355	4	inequalities	inequality	NOUN
ejpam-6985	355	5	and	and	CCONJ
ejpam-6985	355	6	ricci	ricci	PROPN
ejpam-6985	355	7	lower	low	ADJ
ejpam-6985	355	8	bounds	bound	NOUN
ejpam-6985	355	9	for	for	ADP
ejpam-6985	355	10	sub	sub	ADJ
ejpam-6985	355	11	-	-	ADJ
ejpam-6985	355	12	riemannian	riemannian	ADJ
ejpam-6985	355	13	manifolds	manifold	NOUN
ejpam-6985	355	14	with	with	ADP
ejpam-6985	355	15	transverse	transverse	NOUN
ejpam-6985	355	16	symmetries	symmetry	NOUN
ejpam-6985	355	17	.	.	PUNCT
ejpam-6985	356	1	j.	j.	PROPN
ejpam-6985	356	2	eur	eur	PROPN
ejpam-6985	356	3	.	.	PUNCT
ejpam-6985	356	4	math	math	PROPN
ejpam-6985	356	5	.	.	PUNCT
ejpam-6985	357	1	soc	soc	PROPN
ejpam-6985	357	2	.	.	PUNCT
ejpam-6985	357	3	,	,	PUNCT
ejpam-6985	357	4	19:151	19:151	NUM
ejpam-6985	357	5	–	–	PUNCT
ejpam-6985	357	6	219	219	NUM
ejpam-6985	357	7	,	,	PUNCT
ejpam-6985	357	8	2017	2017	NUM
ejpam-6985	357	9	.	.	PUNCT
ejpam-6985	358	1	[	[	X
ejpam-6985	358	2	9	9	NUM
ejpam-6985	358	3	]	]	X
ejpam-6985	358	4	r.	r.	PROPN
ejpam-6985	358	5	l.	l.	PROPN
ejpam-6985	358	6	frank	frank	PROPN
ejpam-6985	358	7	and	and	CCONJ
ejpam-6985	358	8	e.	e.	PROPN
ejpam-6985	358	9	h.	h.	PROPN
ejpam-6985	358	10	lieb	lieb	PROPN
ejpam-6985	358	11	.	.	PUNCT
ejpam-6985	359	1	sharp	sharp	ADJ
ejpam-6985	359	2	constants	constant	NOUN
ejpam-6985	359	3	in	in	ADP
ejpam-6985	359	4	several	several	ADJ
ejpam-6985	359	5	inequalities	inequality	NOUN
ejpam-6985	359	6	on	on	ADP
ejpam-6985	359	7	the	the	DET
ejpam-6985	359	8	heisenberg	heisenberg	PROPN
ejpam-6985	359	9	group	group	NOUN
ejpam-6985	359	10	.	.	PUNCT
ejpam-6985	360	1	ann	ann	PROPN
ejpam-6985	360	2	.	.	PROPN
ejpam-6985	360	3	of	of	ADP
ejpam-6985	360	4	math	math	NOUN
ejpam-6985	360	5	.	.	PUNCT
ejpam-6985	361	1	(	(	PUNCT
ejpam-6985	361	2	2	2	NUM
ejpam-6985	361	3	)	)	PUNCT
ejpam-6985	361	4	,	,	PUNCT
ejpam-6985	361	5	176:349–381	176:349–381	NUM
ejpam-6985	361	6	,	,	PUNCT
ejpam-6985	361	7	2012	2012	NUM
ejpam-6985	361	8	.	.	PUNCT
ejpam-6985	362	1	[	[	X
ejpam-6985	362	2	10	10	NUM
ejpam-6985	362	3	]	]	PUNCT
ejpam-6985	362	4	luigi	luigi	PROPN
ejpam-6985	362	5	ambrosio	ambrosio	PROPN
ejpam-6985	362	6	,	,	PUNCT
ejpam-6985	362	7	roberta	roberta	PROPN
ejpam-6985	362	8	ghezzi	ghezzi	NOUN
ejpam-6985	362	9	,	,	PUNCT
ejpam-6985	362	10	and	and	CCONJ
ejpam-6985	362	11	valentino	valentino	PROPN
ejpam-6985	362	12	magnani	magnani	PROPN
ejpam-6985	362	13	.	.	PUNCT
ejpam-6985	363	1	bv	bv	PROPN
ejpam-6985	363	2	functions	function	NOUN
ejpam-6985	363	3	and	and	CCONJ
ejpam-6985	363	4	sets	set	NOUN
ejpam-6985	363	5	of	of	ADP
ejpam-6985	363	6	finite	finite	ADJ
ejpam-6985	363	7	perimeter	perimeter	NOUN
ejpam-6985	363	8	in	in	ADP
ejpam-6985	363	9	sub	sub	ADJ
ejpam-6985	363	10	-	-	ADJ
ejpam-6985	363	11	riemannian	riemannian	ADJ
ejpam-6985	363	12	manifolds	manifold	NOUN
ejpam-6985	363	13	.	.	PUNCT
ejpam-6985	364	1	annales	annales	PROPN
ejpam-6985	364	2	de	de	PROPN
ejpam-6985	364	3	l’institut	l’institut	PROPN
ejpam-6985	364	4	henri	henri	PROPN
ejpam-6985	365	1	poincaré	poincaré	ADJ
ejpam-6985	365	2	c	c	X
ejpam-6985	365	3	,	,	PUNCT
ejpam-6985	365	4	analyse	analyse	VERB
ejpam-6985	365	5	non	non	ADJ
ejpam-6985	365	6	linéaire	linéaire	PROPN
ejpam-6985	365	7	,	,	PUNCT
ejpam-6985	365	8	32(3):489–517	32(3):489–517	PROPN
ejpam-6985	365	9	,	,	PUNCT
ejpam-6985	365	10	2015	2015	NUM
ejpam-6985	365	11	.	.	PUNCT
ejpam-6985	366	1	[	[	X
ejpam-6985	366	2	11	11	NUM
ejpam-6985	366	3	]	]	X
ejpam-6985	366	4	d.	d.	PROPN
ejpam-6985	366	5	jerison	jerison	PROPN
ejpam-6985	366	6	and	and	CCONJ
ejpam-6985	366	7	a.	a.	PROPN
ejpam-6985	366	8	sánchez	sánchez	PROPN
ejpam-6985	366	9	-	-	PUNCT
ejpam-6985	366	10	calle	calle	PROPN
ejpam-6985	366	11	.	.	PUNCT
ejpam-6985	367	1	subelliptic	subelliptic	ADJ
ejpam-6985	367	2	,	,	PUNCT
ejpam-6985	367	3	second	second	ADJ
ejpam-6985	367	4	order	order	NOUN
ejpam-6985	367	5	differential	differential	NOUN
ejpam-6985	367	6	operators	operator	NOUN
ejpam-6985	367	7	.	.	PUNCT
ejpam-6985	368	1	in	in	ADP
ejpam-6985	368	2	lecture	lecture	NOUN
ejpam-6985	368	3	notes	note	NOUN
ejpam-6985	368	4	in	in	ADP
ejpam-6985	368	5	math	math	NOUN
ejpam-6985	368	6	.	.	PUNCT
ejpam-6985	368	7	,	,	PUNCT
ejpam-6985	368	8	volume	volume	NOUN
ejpam-6985	368	9	1324	1324	NUM
ejpam-6985	368	10	,	,	PUNCT
ejpam-6985	368	11	pages	page	NOUN
ejpam-6985	368	12	46–77	46–77	NUM
ejpam-6985	368	13	.	.	PUNCT
ejpam-6985	368	14	springer	springer	NOUN
ejpam-6985	368	15	,	,	PUNCT
ejpam-6985	368	16	1987	1987	NUM
ejpam-6985	368	17	.	.	PUNCT
ejpam-6985	369	1	[	[	X
ejpam-6985	369	2	12	12	NUM
ejpam-6985	369	3	]	]	X
ejpam-6985	369	4	sorin	sorin	NOUN
ejpam-6985	369	5	dragomir	dragomir	NOUN
ejpam-6985	369	6	and	and	CCONJ
ejpam-6985	369	7	giuseppe	giuseppe	PROPN
ejpam-6985	369	8	tomassini	tomassini	PROPN
ejpam-6985	369	9	.	.	PUNCT
ejpam-6985	369	10	differential	differential	ADJ
ejpam-6985	369	11	geometry	geometry	NOUN
ejpam-6985	369	12	and	and	CCONJ
ejpam-6985	369	13	analysis	analysis	NOUN
ejpam-6985	369	14	on	on	ADP
ejpam-6985	369	15	cr	cr	PROPN
ejpam-6985	369	16	manifolds	manifold	NOUN
ejpam-6985	369	17	.	.	PUNCT
ejpam-6985	370	1	2006	2006	NUM
ejpam-6985	370	2	.	.	PUNCT
ejpam-6985	371	1	[	[	X
ejpam-6985	371	2	13	13	NUM
ejpam-6985	371	3	]	]	PUNCT
ejpam-6985	371	4	l.	l.	PROPN
ejpam-6985	371	5	saloff	saloff	PROPN
ejpam-6985	371	6	-	-	PUNCT
ejpam-6985	371	7	coste	coste	NOUN
ejpam-6985	371	8	.	.	PUNCT
ejpam-6985	371	9	aspects	aspect	NOUN
ejpam-6985	371	10	of	of	ADP
ejpam-6985	371	11	sobolev	sobolev	NOUN
ejpam-6985	371	12	-	-	PUNCT
ejpam-6985	371	13	type	type	NOUN
ejpam-6985	371	14	inequalities	inequality	NOUN
ejpam-6985	371	15	.	.	PUNCT
ejpam-6985	372	1	289	289	NUM
ejpam-6985	372	2	,	,	PUNCT
ejpam-6985	372	3	2002	2002	NUM
ejpam-6985	372	4	.	.	PUNCT
ejpam-6985	373	1	[	[	X
ejpam-6985	373	2	14	14	NUM
ejpam-6985	373	3	]	]	X
ejpam-6985	373	4	h.	h.	PROPN
ejpam-6985	373	5	rossi	rossi	PROPN
ejpam-6985	373	6	.	.	PUNCT
ejpam-6985	374	1	attaching	attach	VERB
ejpam-6985	374	2	analytic	analytic	ADJ
ejpam-6985	374	3	spaces	space	NOUN
ejpam-6985	374	4	to	to	ADP
ejpam-6985	374	5	an	an	DET
ejpam-6985	374	6	analytic	analytic	ADJ
ejpam-6985	374	7	space	space	NOUN
ejpam-6985	374	8	along	along	ADP
ejpam-6985	374	9	a	a	DET
ejpam-6985	374	10	pseudoconcave	pseudoconcave	NOUN
ejpam-6985	374	11	boundary	boundary	NOUN
ejpam-6985	374	12	.	.	PUNCT
ejpam-6985	375	1	in	in	ADP
ejpam-6985	375	2	proc	proc	PROPN
ejpam-6985	375	3	.	.	PUNCT
ejpam-6985	376	1	conf	conf	NOUN
ejpam-6985	376	2	.	.	PUNCT
ejpam-6985	377	1	complex	complex	ADJ
ejpam-6985	377	2	analysis	analysis	NOUN
ejpam-6985	377	3	(	(	PUNCT
ejpam-6985	377	4	minneapolis	minneapolis	NOUN
ejpam-6985	377	5	,	,	PUNCT
ejpam-6985	377	6	1964	1964	NUM
ejpam-6985	377	7	)	)	PUNCT
ejpam-6985	377	8	,	,	PUNCT
ejpam-6985	377	9	pages	page	VERB
ejpam-6985	377	10	242–256	242–256	NUM
ejpam-6985	377	11	.	.	PUNCT
ejpam-6985	378	1	springer	springer	NOUN
ejpam-6985	378	2	lecture	lecture	NOUN
ejpam-6985	378	3	notes	note	NOUN
ejpam-6985	378	4	,	,	PUNCT
ejpam-6985	378	5	1965	1965	NUM
ejpam-6985	378	6	.	.	PUNCT
ejpam-6985	379	1	a.	a.	PROPN
ejpam-6985	379	2	ben	ben	PROPN
ejpam-6985	379	3	ahmed	ahmed	PROPN
ejpam-6985	379	4	/	/	SYM
ejpam-6985	379	5	eur	eur	PROPN
ejpam-6985	379	6	.	.	PUNCT
ejpam-6985	380	1	j.	j.	PROPN
ejpam-6985	380	2	pure	pure	PROPN
ejpam-6985	380	3	appl	appl	PROPN
ejpam-6985	380	4	.	.	PROPN
ejpam-6985	380	5	math	math	PROPN
ejpam-6985	380	6	,	,	PUNCT
ejpam-6985	380	7	18	18	NUM
ejpam-6985	380	8	(	(	PUNCT
ejpam-6985	380	9	4	4	NUM
ejpam-6985	380	10	)	)	PUNCT
ejpam-6985	380	11	(	(	PUNCT
ejpam-6985	380	12	2025	2025	NUM
ejpam-6985	380	13	)	)	PUNCT
ejpam-6985	380	14	,	,	PUNCT
ejpam-6985	380	15	6985	6985	NUM
ejpam-6985	380	16	16	16	NUM
ejpam-6985	380	17	of	of	ADP
ejpam-6985	380	18	16	16	NUM
ejpam-6985	381	1	[	[	X
ejpam-6985	381	2	15	15	NUM
ejpam-6985	381	3	]	]	PUNCT
ejpam-6985	381	4	x.	x.	PROPN
ejpam-6985	381	5	huang	huang	PROPN
ejpam-6985	381	6	and	and	CCONJ
ejpam-6985	381	7	y.-t	y.-t	NOUN
ejpam-6985	381	8	.	.	PUNCT
ejpam-6985	382	1	siu	siu	NOUN
ejpam-6985	382	2	.	.	PUNCT
ejpam-6985	383	1	non	non	ADJ
ejpam-6985	383	2	-	-	ADJ
ejpam-6985	383	3	embeddability	embeddability	NOUN
ejpam-6985	383	4	of	of	ADP
ejpam-6985	383	5	certain	certain	ADJ
ejpam-6985	383	6	abstract	abstract	ADJ
ejpam-6985	383	7	cr	cr	PROPN
ejpam-6985	383	8	manifolds	manifolds	PROPN
ejpam-6985	383	9	.	.	PUNCT
ejpam-6985	384	1	invent	invent	NOUN
ejpam-6985	384	2	.	.	PUNCT
ejpam-6985	385	1	math	math	NOUN
ejpam-6985	385	2	.	.	PUNCT
ejpam-6985	385	3	,	,	PUNCT
ejpam-6985	385	4	122:1–27	122:1–27	NUM
ejpam-6985	385	5	,	,	PUNCT
ejpam-6985	385	6	1995	1995	NUM
ejpam-6985	385	7	.	.	PUNCT
ejpam-6985	386	1	[	[	X
ejpam-6985	386	2	16	16	NUM
ejpam-6985	386	3	]	]	PUNCT
ejpam-6985	386	4	h.bosch	h.bosch	PROPN
ejpam-6985	386	5	,	,	PUNCT
ejpam-6985	386	6	t.gonzales	t.gonzale	NOUN
ejpam-6985	386	7	,	,	PUNCT
ejpam-6985	386	8	k.spinelli	k.spinelli	PROPN
ejpam-6985	386	9	,	,	PUNCT
ejpam-6985	386	10	g.udell	g.udell	NOUN
ejpam-6985	386	11	,	,	PUNCT
ejpam-6985	386	12	and	and	CCONJ
ejpam-6985	386	13	y.e	y.e	PROPN
ejpam-6985	386	14	.	.	PROPN
ejpam-6985	387	1	zeytuncu	zeytuncu	PROPN
ejpam-6985	387	2	.	.	PUNCT
ejpam-6985	388	1	cr	cr	PROPN
ejpam-6985	388	2	embeddability	embeddability	NOUN
ejpam-6985	388	3	of	of	ADP
ejpam-6985	388	4	quotients	quotient	NOUN
ejpam-6985	388	5	of	of	ADP
ejpam-6985	388	6	the	the	DET
ejpam-6985	388	7	rossi	rossi	PROPN
ejpam-6985	388	8	sphere	sphere	NOUN
ejpam-6985	388	9	via	via	ADP
ejpam-6985	388	10	spectral	spectral	ADJ
ejpam-6985	388	11	theory	theory	NOUN
ejpam-6985	388	12	.	.	PUNCT
ejpam-6985	389	1	international	international	ADJ
ejpam-6985	389	2	journal	journal	PROPN
ejpam-6985	389	3	of	of	ADP
ejpam-6985	389	4	mathematics	mathematic	NOUN
ejpam-6985	389	5	,	,	PUNCT
ejpam-6985	389	6	33(02):2250014	33(02):2250014	NUM
ejpam-6985	389	7	,	,	PUNCT
ejpam-6985	389	8	2022	2022	NUM
ejpam-6985	389	9	.	.	PUNCT
ejpam-6985	390	1	[	[	X
ejpam-6985	390	2	17	17	NUM
ejpam-6985	390	3	]	]	PUNCT
ejpam-6985	390	4	t.	t.	PROPN
ejpam-6985	390	5	kato	kato	PROPN
ejpam-6985	390	6	.	.	PUNCT
ejpam-6985	390	7	perturbation	perturbation	NOUN
ejpam-6985	390	8	theory	theory	NOUN
ejpam-6985	390	9	for	for	ADP
ejpam-6985	390	10	linear	linear	PROPN
ejpam-6985	390	11	operators	operator	NOUN
ejpam-6985	390	12	.	.	PUNCT
ejpam-6985	391	1	1995	1995	NUM
ejpam-6985	391	2	.	.	PUNCT