id	sid	tid	token	lemma	pos
ejde-1401	1	1	electronic	electronic	ADJ
ejde-1401	1	2	journal	journal	NOUN
ejde-1401	1	3	of	of	ADP
ejde-1401	1	4	differential	differential	ADJ
ejde-1401	1	5	equations	equation	NOUN
ejde-1401	1	6	,	,	PUNCT
ejde-1401	1	7	vol	vol	NOUN
ejde-1401	1	8	.	.	PUNCT
ejde-1401	1	9	2025	2025	NUM
ejde-1401	1	10	(	(	PUNCT
ejde-1401	1	11	2025	2025	NUM
ejde-1401	1	12	)	)	PUNCT
ejde-1401	1	13	,	,	PUNCT
ejde-1401	1	14	no	no	INTJ
ejde-1401	1	15	.	.	NOUN
ejde-1401	1	16	62	62	NUM
ejde-1401	1	17	,	,	PUNCT
ejde-1401	1	18	pp	pp	ADJ
ejde-1401	1	19	.	.	PUNCT
ejde-1401	2	1	1–10	1–10	PROPN
ejde-1401	2	2	.	.	PUNCT
ejde-1401	3	1	issn	issn	PROPN
ejde-1401	3	2	:	:	PUNCT
ejde-1401	3	3	1072	1072	NUM
ejde-1401	3	4	-	-	SYM
ejde-1401	3	5	6691	6691	NUM
ejde-1401	3	6	.	.	PUNCT
ejde-1401	4	1	url	url	PROPN
ejde-1401	4	2	:	:	PUNCT
ejde-1401	4	3	https://ejde.math.txstate.edu	https://ejde.math.txstate.edu	PROPN
ejde-1401	4	4	,	,	PUNCT
ejde-1401	4	5	https://ejde.math.unt.edu	https://ejde.math.unt.edu	PROPN
ejde-1401	4	6	doi	doi	PROPN
ejde-1401	4	7	:	:	PUNCT
ejde-1401	4	8	10.58997	10.58997	NUM
ejde-1401	4	9	/	/	SYM
ejde-1401	4	10	ejde.2025.62	ejde.2025.62	NOUN
ejde-1401	4	11	complete	complete	ADJ
ejde-1401	4	12	noncompact	noncompact	NOUN
ejde-1401	4	13	and	and	CCONJ
ejde-1401	4	14	stochastically	stochastically	ADV
ejde-1401	4	15	complete	complete	ADJ
ejde-1401	4	16	m	m	NOUN
ejde-1401	4	17	-	-	PUNCT
ejde-1401	4	18	quasi	quasi	ADJ
ejde-1401	4	19	yamabe	yamabe	PROPN
ejde-1401	4	20	gradient	gradient	PROPN
ejde-1401	4	21	solitons	solitons	PROPN
ejde-1401	4	22	giovanni	giovanni	PROPN
ejde-1401	4	23	molica	molica	PROPN
ejde-1401	4	24	bisci	bisci	PROPN
ejde-1401	4	25	,	,	PUNCT
ejde-1401	4	26	henrique	henrique	PROPN
ejde-1401	4	27	f.	f.	PROPN
ejde-1401	4	28	de	de	PROPN
ejde-1401	4	29	lima	lima	PROPN
ejde-1401	4	30	,	,	PUNCT
ejde-1401	4	31	ary	ary	PROPN
ejde-1401	4	32	v.	v.	PROPN
ejde-1401	4	33	f.	f.	PROPN
ejde-1401	4	34	leite	leite	PROPN
ejde-1401	4	35	,	,	PUNCT
ejde-1401	4	36	marco	marco	PROPN
ejde-1401	4	37	a.	a.	PROPN
ejde-1401	4	38	l.	l.	PROPN
ejde-1401	4	39	velásquez	velásquez	PROPN
ejde-1401	4	40	abstract	abstract	PROPN
ejde-1401	4	41	.	.	PUNCT
ejde-1401	5	1	we	we	PRON
ejde-1401	5	2	establish	establish	VERB
ejde-1401	5	3	new	new	ADJ
ejde-1401	5	4	characterization	characterization	NOUN
ejde-1401	5	5	and	and	CCONJ
ejde-1401	5	6	nonexistence	nonexistence	NOUN
ejde-1401	5	7	results	result	NOUN
ejde-1401	5	8	concerning	concern	VERB
ejde-1401	5	9	complete	complete	ADJ
ejde-1401	5	10	noncompact	noncompact	NOUN
ejde-1401	5	11	and	and	CCONJ
ejde-1401	5	12	stochastically	stochastically	ADV
ejde-1401	5	13	complete	complete	ADJ
ejde-1401	5	14	m	m	NOUN
ejde-1401	5	15	-	-	PUNCT
ejde-1401	5	16	quasi	quasi	ADJ
ejde-1401	5	17	yamabe	yamabe	PROPN
ejde-1401	5	18	gradient	gradient	PROPN
ejde-1401	5	19	solitons	soliton	NOUN
ejde-1401	5	20	through	through	ADP
ejde-1401	5	21	the	the	DET
ejde-1401	5	22	applications	application	NOUN
ejde-1401	5	23	of	of	ADP
ejde-1401	5	24	a	a	DET
ejde-1401	5	25	key	key	ADJ
ejde-1401	5	26	bochner	bochner	NOUN
ejde-1401	5	27	type	type	NOUN
ejde-1401	5	28	formula	formula	NOUN
ejde-1401	5	29	jointly	jointly	ADV
ejde-1401	5	30	with	with	ADP
ejde-1401	5	31	suitable	suitable	ADJ
ejde-1401	5	32	maximum	maximum	ADJ
ejde-1401	5	33	principles	principle	NOUN
ejde-1401	5	34	dealing	deal	VERB
ejde-1401	5	35	,	,	PUNCT
ejde-1401	5	36	in	in	ADP
ejde-1401	5	37	particular	particular	ADJ
ejde-1401	5	38	,	,	PUNCT
ejde-1401	5	39	with	with	ADP
ejde-1401	5	40	the	the	DET
ejde-1401	5	41	notions	notion	NOUN
ejde-1401	5	42	of	of	ADP
ejde-1401	5	43	convergence	convergence	NOUN
ejde-1401	5	44	to	to	ADP
ejde-1401	5	45	zero	zero	NUM
ejde-1401	5	46	at	at	ADP
ejde-1401	5	47	infinity	infinity	NOUN
ejde-1401	5	48	and	and	CCONJ
ejde-1401	5	49	polynomial	polynomial	ADJ
ejde-1401	5	50	and	and	CCONJ
ejde-1401	5	51	exponential	exponential	ADJ
ejde-1401	5	52	volume	volume	NOUN
ejde-1401	5	53	growth	growth	NOUN
ejde-1401	5	54	.	.	PUNCT
ejde-1401	6	1	1	1	X
ejde-1401	6	2	.	.	X
ejde-1401	6	3	introduction	introduction	NOUN
ejde-1401	6	4	in	in	ADP
ejde-1401	6	5	1960	1960	NUM
ejde-1401	6	6	,	,	PUNCT
ejde-1401	6	7	using	use	VERB
ejde-1401	6	8	calculus	calculus	NOUN
ejde-1401	6	9	of	of	ADP
ejde-1401	6	10	variations	variation	NOUN
ejde-1401	6	11	and	and	CCONJ
ejde-1401	6	12	elliptic	elliptic	ADJ
ejde-1401	6	13	partial	partial	ADJ
ejde-1401	6	14	differential	differential	NOUN
ejde-1401	6	15	equations	equation	NOUN
ejde-1401	6	16	techniques	technique	NOUN
ejde-1401	6	17	,	,	PUNCT
ejde-1401	6	18	yamabe	yamabe	ADJ
ejde-1401	6	19	[	[	X
ejde-1401	6	20	27	27	NUM
ejde-1401	6	21	]	]	PUNCT
ejde-1401	6	22	believed	believe	VERB
ejde-1401	6	23	he	he	PRON
ejde-1401	6	24	had	have	AUX
ejde-1401	6	25	solved	solve	VERB
ejde-1401	6	26	the	the	DET
ejde-1401	6	27	following	follow	VERB
ejde-1401	6	28	problem	problem	NOUN
ejde-1401	6	29	(	(	PUNCT
ejde-1401	6	30	also	also	ADV
ejde-1401	6	31	known	know	VERB
ejde-1401	6	32	as	as	ADP
ejde-1401	6	33	yamabe	yamabe	ADJ
ejde-1401	6	34	problem	problem	NOUN
ejde-1401	6	35	):	):	PUNCT
ejde-1401	6	36	every	every	DET
ejde-1401	6	37	compact	compact	ADJ
ejde-1401	6	38	riemannian	riemannian	NOUN
ejde-1401	6	39	manifold	manifold	NOUN
ejde-1401	6	40	has	have	VERB
ejde-1401	6	41	a	a	DET
ejde-1401	6	42	conformal	conformal	ADJ
ejde-1401	6	43	metric	metric	NOUN
ejde-1401	6	44	of	of	ADP
ejde-1401	6	45	constant	constant	ADJ
ejde-1401	6	46	scalar	scalar	ADJ
ejde-1401	6	47	curvature	curvature	NOUN
ejde-1401	6	48	.	.	PUNCT
ejde-1401	7	1	however	however	ADV
ejde-1401	7	2	,	,	PUNCT
ejde-1401	7	3	in	in	ADP
ejde-1401	7	4	1968	1968	NUM
ejde-1401	7	5	trudinger	trudinger	NOUN
ejde-1401	8	1	[	[	X
ejde-1401	8	2	25	25	NUM
ejde-1401	8	3	]	]	PUNCT
ejde-1401	8	4	discovered	discover	VERB
ejde-1401	8	5	an	an	DET
ejde-1401	8	6	error	error	NOUN
ejde-1401	8	7	in	in	ADP
ejde-1401	8	8	yamabe	yamabe	NOUN
ejde-1401	8	9	’s	’s	PART
ejde-1401	8	10	proof	proof	NOUN
ejde-1401	8	11	.	.	PUNCT
ejde-1401	9	1	independently	independently	ADV
ejde-1401	9	2	,	,	PUNCT
ejde-1401	9	3	trudinger	trudinger	NOUN
ejde-1401	9	4	[	[	X
ejde-1401	9	5	25	25	NUM
ejde-1401	9	6	]	]	PUNCT
ejde-1401	9	7	and	and	CCONJ
ejde-1401	9	8	aubin	aubin	PROPN
ejde-1401	10	1	[	[	X
ejde-1401	10	2	4	4	X
ejde-1401	10	3	]	]	PUNCT
ejde-1401	10	4	contributed	contribute	VERB
ejde-1401	10	5	to	to	ADP
ejde-1401	10	6	the	the	DET
ejde-1401	10	7	yamabe	yamabe	ADJ
ejde-1401	10	8	problem	problem	NOUN
ejde-1401	10	9	showing	show	VERB
ejde-1401	10	10	that	that	SCONJ
ejde-1401	10	11	it	it	PRON
ejde-1401	10	12	can	can	AUX
ejde-1401	10	13	be	be	AUX
ejde-1401	10	14	solved	solve	VERB
ejde-1401	10	15	on	on	ADP
ejde-1401	10	16	any	any	DET
ejde-1401	10	17	compact	compact	ADJ
ejde-1401	10	18	manifold	manifold	ADJ
ejde-1401	10	19	σn	σn	NOUN
ejde-1401	10	20	with	with	ADP
ejde-1401	10	21	the	the	DET
ejde-1401	10	22	additional	additional	ADJ
ejde-1401	10	23	assumption	assumption	NOUN
ejde-1401	10	24	that	that	SCONJ
ejde-1401	10	25	the	the	DET
ejde-1401	10	26	yamabe	yamabe	ADJ
ejde-1401	10	27	invariant	invariant	NOUN
ejde-1401	10	28	of	of	ADP
ejde-1401	10	29	σn	σn	NOUN
ejde-1401	10	30	is	be	AUX
ejde-1401	10	31	less	less	ADJ
ejde-1401	10	32	than	than	ADP
ejde-1401	10	33	the	the	DET
ejde-1401	10	34	yamabe	yamabe	ADJ
ejde-1401	10	35	invariant	invariant	NOUN
ejde-1401	10	36	of	of	ADP
ejde-1401	10	37	the	the	DET
ejde-1401	10	38	round	round	NOUN
ejde-1401	10	39	sphere	sphere	NOUN
ejde-1401	10	40	.	.	PUNCT
ejde-1401	11	1	moreover	moreover	ADV
ejde-1401	11	2	,	,	PUNCT
ejde-1401	11	3	aubin	aubin	PROPN
ejde-1401	11	4	also	also	ADV
ejde-1401	11	5	showed	show	VERB
ejde-1401	11	6	that	that	SCONJ
ejde-1401	11	7	if	if	SCONJ
ejde-1401	11	8	σn	σn	NOUN
ejde-1401	11	9	has	have	VERB
ejde-1401	11	10	dimension	dimension	NOUN
ejde-1401	11	11	n	n	PRON
ejde-1401	11	12	≥	≥	NOUN
ejde-1401	11	13	6	6	NUM
ejde-1401	11	14	and	and	CCONJ
ejde-1401	11	15	it	it	PRON
ejde-1401	11	16	is	be	AUX
ejde-1401	11	17	not	not	PART
ejde-1401	11	18	locally	locally	ADV
ejde-1401	11	19	conformallly	conformallly	ADV
ejde-1401	11	20	flat	flat	ADJ
ejde-1401	11	21	,	,	PUNCT
ejde-1401	11	22	then	then	ADV
ejde-1401	11	23	the	the	DET
ejde-1401	11	24	yamabe	yamabe	ADJ
ejde-1401	11	25	invariant	invariant	NOUN
ejde-1401	11	26	of	of	ADP
ejde-1401	11	27	σn	σn	NOUN
ejde-1401	11	28	is	be	AUX
ejde-1401	11	29	less	less	ADJ
ejde-1401	11	30	than	than	ADP
ejde-1401	11	31	the	the	DET
ejde-1401	11	32	yamabe	yamabe	ADJ
ejde-1401	11	33	invariant	invariant	NOUN
ejde-1401	11	34	of	of	ADP
ejde-1401	11	35	the	the	DET
ejde-1401	11	36	round	round	NOUN
ejde-1401	11	37	sphere	sphere	NOUN
ejde-1401	11	38	.	.	PUNCT
ejde-1401	12	1	in	in	ADP
ejde-1401	12	2	1984	1984	NUM
ejde-1401	12	3	,	,	PUNCT
ejde-1401	12	4	schoen	schoen	NOUN
ejde-1401	12	5	[	[	X
ejde-1401	12	6	23	23	NUM
ejde-1401	12	7	]	]	PUNCT
ejde-1401	12	8	completed	complete	VERB
ejde-1401	12	9	the	the	DET
ejde-1401	12	10	solution	solution	NOUN
ejde-1401	12	11	of	of	ADP
ejde-1401	12	12	yamabe	yamabe	ADJ
ejde-1401	12	13	problem	problem	NOUN
ejde-1401	12	14	showing	show	VERB
ejde-1401	12	15	that	that	SCONJ
ejde-1401	12	16	if	if	SCONJ
ejde-1401	12	17	σn	σn	NOUN
ejde-1401	12	18	has	have	VERB
ejde-1401	12	19	dimension	dimension	NOUN
ejde-1401	12	20	n	n	PRON
ejde-1401	12	21	∈	∈	PROPN
ejde-1401	12	22	{	{	PUNCT
ejde-1401	12	23	3	3	NUM
ejde-1401	12	24	,	,	PUNCT
ejde-1401	12	25	4	4	NUM
ejde-1401	12	26	,	,	PUNCT
ejde-1401	12	27	5	5	NUM
ejde-1401	12	28	}	}	PUNCT
ejde-1401	12	29	or	or	CCONJ
ejde-1401	12	30	if	if	SCONJ
ejde-1401	12	31	σn	σn	PRON
ejde-1401	12	32	is	be	AUX
ejde-1401	12	33	locally	locally	ADV
ejde-1401	12	34	conformally	conformally	ADV
ejde-1401	12	35	flat	flat	ADJ
ejde-1401	12	36	,	,	PUNCT
ejde-1401	12	37	then	then	ADV
ejde-1401	12	38	the	the	DET
ejde-1401	12	39	yamabe	yamabe	ADJ
ejde-1401	12	40	invariant	invariant	NOUN
ejde-1401	12	41	of	of	ADP
ejde-1401	12	42	σn	σn	NOUN
ejde-1401	12	43	is	be	AUX
ejde-1401	12	44	less	less	ADJ
ejde-1401	12	45	than	than	ADP
ejde-1401	12	46	the	the	DET
ejde-1401	12	47	yamabe	yamabe	ADJ
ejde-1401	12	48	invariant	invariant	NOUN
ejde-1401	12	49	of	of	ADP
ejde-1401	12	50	the	the	DET
ejde-1401	12	51	round	round	NOUN
ejde-1401	12	52	sphere	sphere	NOUN
ejde-1401	12	53	,	,	PUNCT
ejde-1401	12	54	unless	unless	SCONJ
ejde-1401	12	55	σ	σ	PROPN
ejde-1401	12	56	is	be	AUX
ejde-1401	12	57	conformal	conformal	ADJ
ejde-1401	12	58	to	to	ADP
ejde-1401	12	59	the	the	DET
ejde-1401	12	60	round	round	ADJ
ejde-1401	12	61	sphere	sphere	NOUN
ejde-1401	12	62	(	(	PUNCT
ejde-1401	12	63	for	for	ADP
ejde-1401	12	64	more	more	ADJ
ejde-1401	12	65	details	detail	NOUN
ejde-1401	12	66	,	,	PUNCT
ejde-1401	12	67	we	we	PRON
ejde-1401	12	68	recommend	recommend	VERB
ejde-1401	12	69	[	[	X
ejde-1401	12	70	15	15	NUM
ejde-1401	12	71	]	]	NUM
ejde-1401	12	72	)	)	PUNCT
ejde-1401	12	73	.	.	PUNCT
ejde-1401	13	1	afterwards	afterwards	ADV
ejde-1401	13	2	,	,	PUNCT
ejde-1401	13	3	hamilton	hamilton	PROPN
ejde-1401	14	1	[	[	X
ejde-1401	14	2	12	12	NUM
ejde-1401	14	3	]	]	PUNCT
ejde-1401	14	4	introduced	introduce	VERB
ejde-1401	14	5	the	the	DET
ejde-1401	14	6	yamabe	yamabe	ADJ
ejde-1401	14	7	flow	flow	NOUN
ejde-1401	14	8	of	of	ADP
ejde-1401	14	9	a	a	DET
ejde-1401	14	10	riemannian	riemannian	ADJ
ejde-1401	14	11	manifold	manifold	NOUN
ejde-1401	14	12	(	(	PUNCT
ejde-1401	14	13	σn	σn	PROPN
ejde-1401	14	14	,	,	PUNCT
ejde-1401	14	15	g	g	NOUN
ejde-1401	14	16	)	)	PUNCT
ejde-1401	14	17	which	which	PRON
ejde-1401	14	18	describes	describe	VERB
ejde-1401	14	19	how	how	SCONJ
ejde-1401	14	20	the	the	DET
ejde-1401	14	21	metric	metric	ADJ
ejde-1401	14	22	g	g	NOUN
ejde-1401	14	23	is	be	AUX
ejde-1401	14	24	deformed	deform	VERB
ejde-1401	14	25	to	to	ADP
ejde-1401	14	26	a	a	DET
ejde-1401	14	27	metric	metric	ADJ
ejde-1401	14	28	g(t	g(t	PROPN
ejde-1401	14	29	)	)	PUNCT
ejde-1401	14	30	at	at	ADP
ejde-1401	14	31	time	time	NOUN
ejde-1401	14	32	t	t	NOUN
ejde-1401	14	33	through	through	ADP
ejde-1401	14	34	the	the	DET
ejde-1401	14	35	evolution	evolution	NOUN
ejde-1401	14	36	equation	equation	PROPN
ejde-1401	14	37	∂g(t	∂g(t	PROPN
ejde-1401	14	38	)	)	PUNCT
ejde-1401	14	39	∂t	∂t	PROPN
ejde-1401	14	40	=	=	SYM
ejde-1401	14	41	−r(t)g(t	−r(t)g(t	NOUN
ejde-1401	14	42	)	)	PUNCT
ejde-1401	14	43	g(0	g(0	NOUN
ejde-1401	14	44	)	)	PUNCT
ejde-1401	15	1	=	=	SYM
ejde-1401	15	2	g	g	NOUN
ejde-1401	15	3	,	,	PUNCT
ejde-1401	15	4	(	(	PUNCT
ejde-1401	15	5	1.1	1.1	NUM
ejde-1401	15	6	)	)	PUNCT
ejde-1401	15	7	where	where	SCONJ
ejde-1401	15	8	r(t	r(t	NOUN
ejde-1401	15	9	)	)	PUNCT
ejde-1401	15	10	stands	stand	VERB
ejde-1401	15	11	the	the	DET
ejde-1401	15	12	scalar	scalar	ADJ
ejde-1401	15	13	curvature	curvature	NOUN
ejde-1401	15	14	related	relate	VERB
ejde-1401	15	15	to	to	ADP
ejde-1401	15	16	metric	metric	ADJ
ejde-1401	15	17	g(t	g(t	PROPN
ejde-1401	15	18	)	)	PUNCT
ejde-1401	15	19	.	.	PUNCT
ejde-1401	16	1	in	in	ADP
ejde-1401	16	2	this	this	DET
ejde-1401	16	3	branch	branch	NOUN
ejde-1401	16	4	,	,	PUNCT
ejde-1401	16	5	a	a	DET
ejde-1401	16	6	special	special	ADJ
ejde-1401	16	7	solution	solution	NOUN
ejde-1401	16	8	of	of	ADP
ejde-1401	16	9	yamabe	yamabe	ADJ
ejde-1401	16	10	flow	flow	NOUN
ejde-1401	16	11	,	,	PUNCT
ejde-1401	16	12	called	call	VERB
ejde-1401	16	13	yamabe	yamabe	ADJ
ejde-1401	16	14	soliton	soliton	NOUN
ejde-1401	16	15	,	,	PUNCT
ejde-1401	16	16	is	be	AUX
ejde-1401	16	17	a	a	DET
ejde-1401	16	18	self	self	NOUN
ejde-1401	16	19	-	-	PUNCT
ejde-1401	16	20	similar	similar	ADJ
ejde-1401	16	21	solution	solution	NOUN
ejde-1401	16	22	of	of	ADP
ejde-1401	16	23	(	(	PUNCT
ejde-1401	16	24	1.1	1.1	NUM
ejde-1401	16	25	)	)	PUNCT
ejde-1401	16	26	such	such	ADJ
ejde-1401	16	27	that	that	SCONJ
ejde-1401	16	28	1	1	NUM
ejde-1401	16	29	2	2	NUM
ejde-1401	16	30	lxg	lxg	NOUN
ejde-1401	16	31	=	=	PUNCT
ejde-1401	16	32	(	(	PUNCT
ejde-1401	16	33	r−	r−	PROPN
ejde-1401	16	34	ρ)g	ρ)g	ADV
ejde-1401	16	35	,	,	PUNCT
ejde-1401	16	36	(	(	PUNCT
ejde-1401	16	37	1.2	1.2	NUM
ejde-1401	16	38	)	)	PUNCT
ejde-1401	16	39	where	where	SCONJ
ejde-1401	16	40	lxg	lxg	PROPN
ejde-1401	16	41	denotes	denote	VERB
ejde-1401	16	42	the	the	DET
ejde-1401	16	43	lie	lie	NOUN
ejde-1401	16	44	derivative	derivative	NOUN
ejde-1401	16	45	of	of	ADP
ejde-1401	16	46	the	the	DET
ejde-1401	16	47	metric	metric	ADJ
ejde-1401	16	48	g	g	NOUN
ejde-1401	16	49	with	with	ADP
ejde-1401	16	50	the	the	DET
ejde-1401	16	51	respect	respect	NOUN
ejde-1401	16	52	to	to	ADP
ejde-1401	16	53	some	some	DET
ejde-1401	16	54	smooth	smooth	ADJ
ejde-1401	16	55	vector	vector	NOUN
ejde-1401	16	56	field	field	NOUN
ejde-1401	16	57	x	x	X
ejde-1401	16	58	∈	∈	PROPN
ejde-1401	16	59	x(σn	x(σn	PROPN
ejde-1401	16	60	)	)	PUNCT
ejde-1401	16	61	and	and	CCONJ
ejde-1401	16	62	ρ	ρ	NUM
ejde-1401	16	63	∈	∈	PROPN
ejde-1401	16	64	r	r	NOUN
ejde-1401	16	65	is	be	AUX
ejde-1401	16	66	a	a	DET
ejde-1401	16	67	constant	constant	ADJ
ejde-1401	16	68	.	.	PUNCT
ejde-1401	17	1	for	for	ADP
ejde-1401	17	2	the	the	DET
ejde-1401	17	3	particular	particular	ADJ
ejde-1401	17	4	case	case	NOUN
ejde-1401	17	5	that	that	SCONJ
ejde-1401	17	6	x	x	X
ejde-1401	17	7	=	=	SYM
ejde-1401	17	8	∇f	∇f	NOUN
ejde-1401	17	9	,	,	PUNCT
ejde-1401	17	10	where	where	SCONJ
ejde-1401	17	11	∇f	∇f	PROPN
ejde-1401	17	12	denotes	denote	VERB
ejde-1401	17	13	the	the	DET
ejde-1401	17	14	gradient	gradient	NOUN
ejde-1401	17	15	(	(	PUNCT
ejde-1401	17	16	related	relate	VERB
ejde-1401	17	17	to	to	ADP
ejde-1401	17	18	metric	metric	ADJ
ejde-1401	17	19	g	g	NOUN
ejde-1401	17	20	)	)	PUNCT
ejde-1401	17	21	of	of	ADP
ejde-1401	17	22	a	a	DET
ejde-1401	17	23	smooth	smooth	ADJ
ejde-1401	17	24	function	function	NOUN
ejde-1401	17	25	f	f	PROPN
ejde-1401	17	26	∈	∈	PROPN
ejde-1401	17	27	c∞(σn	c∞(σn	NOUN
ejde-1401	17	28	)	)	PUNCT
ejde-1401	17	29	,	,	PUNCT
ejde-1401	17	30	it	it	PRON
ejde-1401	17	31	is	be	AUX
ejde-1401	17	32	called	call	VERB
ejde-1401	17	33	gradient	gradient	ADJ
ejde-1401	17	34	yamabe	yamabe	ADJ
ejde-1401	17	35	soliton	soliton	NOUN
ejde-1401	17	36	and	and	CCONJ
ejde-1401	17	37	(	(	PUNCT
ejde-1401	17	38	1.2	1.2	NUM
ejde-1401	17	39	)	)	PUNCT
ejde-1401	17	40	becomes	become	VERB
ejde-1401	17	41	∇2f	∇2f	PROPN
ejde-1401	17	42	=	=	PUNCT
ejde-1401	17	43	(	(	PUNCT
ejde-1401	17	44	r−	r−	PROPN
ejde-1401	17	45	ρ)g	ρ)g	ADV
ejde-1401	17	46	,	,	PUNCT
ejde-1401	17	47	(	(	PUNCT
ejde-1401	17	48	1.3	1.3	NUM
ejde-1401	17	49	)	)	PUNCT
ejde-1401	17	50	2020	2020	NUM
ejde-1401	17	51	mathematics	mathematic	NOUN
ejde-1401	17	52	subject	subject	ADJ
ejde-1401	17	53	classification	classification	NOUN
ejde-1401	17	54	.	.	PUNCT
ejde-1401	18	1	53c25	53c25	NUM
ejde-1401	18	2	,	,	PUNCT
ejde-1401	18	3	53c44	53c44	NUM
ejde-1401	18	4	.	.	PUNCT
ejde-1401	19	1	key	key	ADJ
ejde-1401	19	2	words	word	NOUN
ejde-1401	19	3	and	and	CCONJ
ejde-1401	19	4	phrases	phrase	NOUN
ejde-1401	19	5	.	.	PUNCT
ejde-1401	20	1	complete	complete	ADJ
ejde-1401	20	2	and	and	CCONJ
ejde-1401	20	3	stochastically	stochastically	ADV
ejde-1401	20	4	complete	complete	ADJ
ejde-1401	20	5	m	m	NOUN
ejde-1401	20	6	-	-	PUNCT
ejde-1401	20	7	quasi	quasi	ADJ
ejde-1401	20	8	yamabe	yamabe	PROPN
ejde-1401	20	9	gradient	gradient	NOUN
ejde-1401	20	10	solitons	soliton	NOUN
ejde-1401	20	11	;	;	PUNCT
ejde-1401	20	12	scalar	scalar	ADJ
ejde-1401	20	13	curvature	curvature	NOUN
ejde-1401	20	14	;	;	PUNCT
ejde-1401	20	15	convergence	convergence	NOUN
ejde-1401	20	16	to	to	ADP
ejde-1401	20	17	zero	zero	NUM
ejde-1401	20	18	at	at	ADP
ejde-1401	20	19	infinity	infinity	NOUN
ejde-1401	20	20	;	;	PUNCT
ejde-1401	20	21	polynomial	polynomial	ADJ
ejde-1401	20	22	and	and	CCONJ
ejde-1401	20	23	exponential	exponential	ADJ
ejde-1401	20	24	volume	volume	NOUN
ejde-1401	20	25	growth	growth	NOUN
ejde-1401	20	26	.	.	PUNCT
ejde-1401	21	1	©	©	PROPN
ejde-1401	21	2	2025	2025	NUM
ejde-1401	21	3	.	.	PUNCT
ejde-1401	22	1	this	this	DET
ejde-1401	22	2	work	work	NOUN
ejde-1401	22	3	is	be	AUX
ejde-1401	22	4	licensed	license	VERB
ejde-1401	22	5	under	under	ADP
ejde-1401	22	6	a	a	DET
ejde-1401	22	7	cc	cc	NOUN
ejde-1401	22	8	by	by	ADP
ejde-1401	22	9	4.0	4.0	NUM
ejde-1401	22	10	license	license	NOUN
ejde-1401	22	11	.	.	PUNCT
ejde-1401	23	1	submitted	submit	VERB
ejde-1401	23	2	april	april	PROPN
ejde-1401	23	3	14	14	NUM
ejde-1401	23	4	,	,	PUNCT
ejde-1401	23	5	2025	2025	NUM
ejde-1401	23	6	.	.	PUNCT
ejde-1401	24	1	published	publish	VERB
ejde-1401	24	2	june	june	PROPN
ejde-1401	24	3	25	25	NUM
ejde-1401	24	4	,	,	PUNCT
ejde-1401	24	5	2025	2025	NUM
ejde-1401	24	6	.	.	PUNCT
ejde-1401	25	1	1	1	NUM
ejde-1401	25	2	2	2	NUM
ejde-1401	25	3	g.	g.	PROPN
ejde-1401	25	4	molica	molica	PROPN
ejde-1401	25	5	bisci	bisci	PROPN
ejde-1401	25	6	,	,	PUNCT
ejde-1401	25	7	h.	h.	PROPN
ejde-1401	25	8	f.	f.	PROPN
ejde-1401	25	9	de	de	PROPN
ejde-1401	25	10	lima	lima	PROPN
ejde-1401	25	11	,	,	PUNCT
ejde-1401	25	12	a.	a.	PROPN
ejde-1401	25	13	v.	v.	PROPN
ejde-1401	25	14	f.	f.	PROPN
ejde-1401	25	15	leite	leite	PROPN
ejde-1401	25	16	,	,	PUNCT
ejde-1401	25	17	m.	m.	NOUN
ejde-1401	25	18	a.	a.	PROPN
ejde-1401	25	19	l.	l.	PROPN
ejde-1401	25	20	velásquez	velásquez	PROPN
ejde-1401	25	21	ejde-2025/62	ejde-2025/62	PROPN
ejde-1401	25	22	where	where	SCONJ
ejde-1401	25	23	∇2f	∇2f	PROPN
ejde-1401	25	24	stands	stand	VERB
ejde-1401	25	25	for	for	ADP
ejde-1401	25	26	the	the	DET
ejde-1401	25	27	hessian	hessian	NOUN
ejde-1401	25	28	(	(	PUNCT
ejde-1401	25	29	related	relate	VERB
ejde-1401	25	30	to	to	ADP
ejde-1401	25	31	metric	metric	ADJ
ejde-1401	25	32	g	g	NOUN
ejde-1401	25	33	)	)	PUNCT
ejde-1401	25	34	of	of	ADP
ejde-1401	25	35	f	f	PROPN
ejde-1401	25	36	.	.	PUNCT
ejde-1401	26	1	a	a	DET
ejde-1401	26	2	first	first	ADJ
ejde-1401	26	3	generalization	generalization	NOUN
ejde-1401	26	4	of	of	ADP
ejde-1401	26	5	the	the	DET
ejde-1401	26	6	gradient	gradient	ADJ
ejde-1401	26	7	yamabe	yamabe	ADJ
ejde-1401	26	8	soliton	soliton	NOUN
ejde-1401	26	9	,	,	PUNCT
ejde-1401	26	10	introduced	introduce	VERB
ejde-1401	26	11	by	by	ADP
ejde-1401	26	12	huang	huang	PROPN
ejde-1401	26	13	and	and	CCONJ
ejde-1401	26	14	li	li	PROPN
ejde-1401	26	15	in	in	ADP
ejde-1401	26	16	[	[	X
ejde-1401	26	17	14	14	NUM
ejde-1401	26	18	]	]	PUNCT
ejde-1401	26	19	,	,	PUNCT
ejde-1401	26	20	is	be	AUX
ejde-1401	26	21	called	call	VERB
ejde-1401	26	22	quasi	quasi	ADJ
ejde-1401	26	23	yamabe	yamabe	PROPN
ejde-1401	26	24	gradient	gradient	PROPN
ejde-1401	26	25	soliton	soliton	NOUN
ejde-1401	26	26	and	and	CCONJ
ejde-1401	26	27	defined	define	VERB
ejde-1401	26	28	by	by	ADP
ejde-1401	26	29	∇2f	∇2f	PROPN
ejde-1401	27	1	−	−	NUM
ejde-1401	27	2	1	1	NUM
ejde-1401	27	3	m	m	NOUN
ejde-1401	27	4	∇f	∇f	NOUN
ejde-1401	27	5	⊗∇f	⊗∇f	NOUN
ejde-1401	27	6	=	=	PUNCT
ejde-1401	27	7	(	(	PUNCT
ejde-1401	27	8	r−	r−	PROPN
ejde-1401	27	9	ρ)g	ρ)g	ADV
ejde-1401	27	10	,	,	PUNCT
ejde-1401	27	11	(	(	PUNCT
ejde-1401	27	12	1.4	1.4	NUM
ejde-1401	27	13	)	)	PUNCT
ejde-1401	27	14	for	for	ADP
ejde-1401	27	15	some	some	DET
ejde-1401	27	16	nonzero	nonzero	ADJ
ejde-1401	27	17	m	m	PROPN
ejde-1401	27	18	∈	∈	PROPN
ejde-1401	27	19	r.	r.	NOUN
ejde-1401	27	20	when	when	SCONJ
ejde-1401	27	21	the	the	DET
ejde-1401	27	22	function	function	NOUN
ejde-1401	27	23	f	f	PROPN
ejde-1401	27	24	is	be	AUX
ejde-1401	27	25	constant	constant	ADJ
ejde-1401	27	26	we	we	PRON
ejde-1401	27	27	say	say	VERB
ejde-1401	27	28	that	that	SCONJ
ejde-1401	27	29	the	the	DET
ejde-1401	27	30	quasi	quasi	PROPN
ejde-1401	27	31	yamabi	yamabi	PROPN
ejde-1401	27	32	gradient	gradient	ADJ
ejde-1401	27	33	soliton	soliton	NOUN
ejde-1401	27	34	is	be	AUX
ejde-1401	27	35	trivial	trivial	ADJ
ejde-1401	27	36	.	.	PUNCT
ejde-1401	28	1	moreover	moreover	ADV
ejde-1401	28	2	,	,	PUNCT
ejde-1401	28	3	it	it	PRON
ejde-1401	28	4	is	be	AUX
ejde-1401	28	5	not	not	PART
ejde-1401	28	6	difficult	difficult	ADJ
ejde-1401	28	7	to	to	PART
ejde-1401	28	8	see	see	VERB
ejde-1401	28	9	that	that	SCONJ
ejde-1401	28	10	when	when	SCONJ
ejde-1401	28	11	m	m	VERB
ejde-1401	28	12	→	→	SYM
ejde-1401	28	13	+	+	NUM
ejde-1401	28	14	∞	∞	NUM
ejde-1401	28	15	the	the	DET
ejde-1401	28	16	equation	equation	NOUN
ejde-1401	28	17	(	(	PUNCT
ejde-1401	28	18	1.4	1.4	NUM
ejde-1401	28	19	)	)	PUNCT
ejde-1401	28	20	returns	return	NOUN
ejde-1401	28	21	to	to	ADP
ejde-1401	28	22	equation	equation	NOUN
ejde-1401	28	23	(	(	PUNCT
ejde-1401	28	24	1.3	1.3	NUM
ejde-1401	28	25	)	)	PUNCT
ejde-1401	28	26	.	.	PUNCT
ejde-1401	29	1	in	in	ADP
ejde-1401	29	2	this	this	DET
ejde-1401	29	3	same	same	ADJ
ejde-1401	29	4	paper	paper	NOUN
ejde-1401	29	5	,	,	PUNCT
ejde-1401	29	6	huang	huang	PROPN
ejde-1401	29	7	and	and	CCONJ
ejde-1401	29	8	li	li	PROPN
ejde-1401	29	9	showed	show	VERB
ejde-1401	29	10	that	that	SCONJ
ejde-1401	29	11	a	a	DET
ejde-1401	29	12	compact	compact	ADJ
ejde-1401	29	13	quasi	quasi	ADJ
ejde-1401	29	14	yamabe	yamabe	PROPN
ejde-1401	29	15	gradient	gradient	PROPN
ejde-1401	29	16	soliton	soliton	NOUN
ejde-1401	29	17	has	have	VERB
ejde-1401	29	18	constant	constant	ADJ
ejde-1401	29	19	scalar	scalar	ADJ
ejde-1401	29	20	curvature	curvature	NOUN
ejde-1401	29	21	,	,	PUNCT
ejde-1401	29	22	extending	extend	VERB
ejde-1401	29	23	a	a	DET
ejde-1401	29	24	previous	previous	ADJ
ejde-1401	29	25	result	result	NOUN
ejde-1401	29	26	due	due	ADP
ejde-1401	29	27	to	to	ADP
ejde-1401	29	28	hsu	hsu	PROPN
ejde-1401	30	1	[	[	X
ejde-1401	30	2	13	13	NUM
ejde-1401	30	3	]	]	PUNCT
ejde-1401	30	4	.	.	PUNCT
ejde-1401	31	1	regarding	regard	VERB
ejde-1401	31	2	to	to	ADP
ejde-1401	31	3	the	the	DET
ejde-1401	31	4	noncompact	noncompact	NOUN
ejde-1401	31	5	case	case	NOUN
ejde-1401	31	6	,	,	PUNCT
ejde-1401	31	7	wang	wang	PROPN
ejde-1401	31	8	[	[	X
ejde-1401	31	9	26	26	NUM
ejde-1401	31	10	]	]	PUNCT
ejde-1401	31	11	gave	give	VERB
ejde-1401	31	12	an	an	DET
ejde-1401	31	13	example	example	NOUN
ejde-1401	31	14	of	of	ADP
ejde-1401	31	15	a	a	DET
ejde-1401	31	16	noncompact	noncompact	ADJ
ejde-1401	31	17	quasi	quasi	ADJ
ejde-1401	31	18	yamabe	yamabe	PROPN
ejde-1401	31	19	gradient	gradient	PROPN
ejde-1401	31	20	soliton	soliton	NOUN
ejde-1401	31	21	with	with	ADP
ejde-1401	31	22	a	a	DET
ejde-1401	31	23	nonconstant	nonconstant	ADJ
ejde-1401	31	24	scalar	scalar	ADJ
ejde-1401	31	25	curvature	curvature	NOUN
ejde-1401	31	26	(	(	PUNCT
ejde-1401	31	27	for	for	ADP
ejde-1401	31	28	more	more	ADJ
ejde-1401	31	29	details	detail	NOUN
ejde-1401	31	30	see	see	VERB
ejde-1401	31	31	[	[	X
ejde-1401	31	32	26	26	NUM
ejde-1401	31	33	,	,	PUNCT
ejde-1401	31	34	example	example	NOUN
ejde-1401	31	35	2.1	2.1	NUM
ejde-1401	31	36	]	]	PUNCT
ejde-1401	31	37	)	)	PUNCT
ejde-1401	31	38	.	.	PUNCT
ejde-1401	32	1	besides	besides	SCONJ
ejde-1401	32	2	,	,	PUNCT
ejde-1401	32	3	among	among	ADP
ejde-1401	32	4	other	other	ADJ
ejde-1401	32	5	results	result	NOUN
ejde-1401	32	6	of	of	ADP
ejde-1401	32	7	this	this	DET
ejde-1401	32	8	work	work	NOUN
ejde-1401	32	9	,	,	PUNCT
ejde-1401	32	10	wang	wang	PROPN
ejde-1401	32	11	showed	show	VERB
ejde-1401	32	12	some	some	DET
ejde-1401	32	13	scalar	scalar	ADJ
ejde-1401	32	14	curvature	curvature	NOUN
ejde-1401	32	15	estimates	estimate	NOUN
ejde-1401	32	16	and	and	CCONJ
ejde-1401	32	17	,	,	PUNCT
ejde-1401	32	18	under	under	ADP
ejde-1401	32	19	a	a	DET
ejde-1401	32	20	suitable	suitable	ADJ
ejde-1401	32	21	integrability	integrability	NOUN
ejde-1401	32	22	condition	condition	NOUN
ejde-1401	32	23	,	,	PUNCT
ejde-1401	32	24	he	he	PRON
ejde-1401	32	25	also	also	ADV
ejde-1401	32	26	proved	prove	VERB
ejde-1401	32	27	that	that	SCONJ
ejde-1401	32	28	a	a	DET
ejde-1401	32	29	quasi	quasi	X
ejde-1401	32	30	yamabe	yamabe	PROPN
ejde-1401	32	31	gradient	gradient	PROPN
ejde-1401	32	32	soliton	soliton	NOUN
ejde-1401	32	33	has	have	VERB
ejde-1401	32	34	constant	constant	ADJ
ejde-1401	32	35	scalar	scalar	ADJ
ejde-1401	32	36	curvature	curvature	NOUN
ejde-1401	32	37	.	.	PUNCT
ejde-1401	33	1	in	in	ADP
ejde-1401	33	2	[	[	X
ejde-1401	33	3	16	16	NUM
ejde-1401	33	4	]	]	PUNCT
ejde-1401	33	5	,	,	PUNCT
ejde-1401	33	6	naik	naik	PROPN
ejde-1401	33	7	introduced	introduce	VERB
ejde-1401	33	8	the	the	DET
ejde-1401	33	9	notion	notion	NOUN
ejde-1401	33	10	of	of	ADP
ejde-1401	33	11	concurrent	concurrent	ADJ
ejde-1401	33	12	-	-	PUNCT
ejde-1401	33	13	recurrent	recurrent	NOUN
ejde-1401	33	14	vector	vector	NOUN
ejde-1401	33	15	field	field	NOUN
ejde-1401	33	16	as	as	ADP
ejde-1401	33	17	a	a	DET
ejde-1401	33	18	vector	vector	NOUN
ejde-1401	33	19	field	field	NOUN
ejde-1401	33	20	ν	ν	NOUN
ejde-1401	33	21	which	which	PRON
ejde-1401	33	22	satisfies	satisfy	VERB
ejde-1401	33	23	the	the	DET
ejde-1401	33	24	relation	relation	NOUN
ejde-1401	33	25	∇xν	∇xν	NOUN
ejde-1401	33	26	=	=	SYM
ejde-1401	33	27	α{x	α{x	ADV
ejde-1401	33	28	−	−	NOUN
ejde-1401	33	29	ν	ν	X
ejde-1401	33	30	♭	♭	PRON
ejde-1401	33	31	(x)ν	(x)ν	NOUN
ejde-1401	33	32	}	}	PUNCT
ejde-1401	33	33	,	,	PUNCT
ejde-1401	33	34	where	where	SCONJ
ejde-1401	33	35	α	α	PROPN
ejde-1401	33	36	∈	∈	PROPN
ejde-1401	33	37	r\{0	r\{0	PROPN
ejde-1401	33	38	}	}	PUNCT
ejde-1401	33	39	and	and	CCONJ
ejde-1401	33	40	ν	ν	DET
ejde-1401	33	41	♭	♭	PROPN
ejde-1401	33	42	is	be	AUX
ejde-1401	33	43	the	the	DET
ejde-1401	33	44	1	1	NUM
ejde-1401	33	45	-	-	PUNCT
ejde-1401	33	46	form	form	NOUN
ejde-1401	33	47	equivalent	equivalent	ADJ
ejde-1401	33	48	to	to	ADP
ejde-1401	33	49	ν	ν	NOUN
ejde-1401	33	50	in	in	ADP
ejde-1401	33	51	a	a	DET
ejde-1401	33	52	riemannian	riemannian	ADJ
ejde-1401	33	53	manifold	manifold	NOUN
ejde-1401	33	54	(	(	PUNCT
ejde-1401	33	55	σn	σn	PROPN
ejde-1401	33	56	,	,	PUNCT
ejde-1401	33	57	g	g	NOUN
ejde-1401	33	58	)	)	PUNCT
ejde-1401	33	59	.	.	PUNCT
ejde-1401	34	1	lately	lately	ADV
ejde-1401	34	2	,	,	PUNCT
ejde-1401	34	3	naik	naik	PROPN
ejde-1401	34	4	,	,	PUNCT
ejde-1401	34	5	ramandi	ramandi	PROPN
ejde-1401	34	6	,	,	PUNCT
ejde-1401	34	7	kumara	kumara	NOUN
ejde-1401	34	8	and	and	CCONJ
ejde-1401	34	9	venkatesha	venkatesha	PROPN
ejde-1401	35	1	[	[	X
ejde-1401	35	2	17	17	NUM
ejde-1401	35	3	]	]	PUNCT
ejde-1401	35	4	used	use	VERB
ejde-1401	35	5	the	the	DET
ejde-1401	35	6	above	above	ADJ
ejde-1401	35	7	concept	concept	NOUN
ejde-1401	35	8	to	to	PART
ejde-1401	35	9	prove	prove	VERB
ejde-1401	35	10	that	that	SCONJ
ejde-1401	35	11	an	an	DET
ejde-1401	35	12	n	n	ADV
ejde-1401	35	13	-	-	PUNCT
ejde-1401	35	14	dimensional	dimensional	ADJ
ejde-1401	35	15	nontrivial	nontrivial	ADJ
ejde-1401	35	16	quasi	quasi	ADJ
ejde-1401	35	17	yamabe	yamabe	PROPN
ejde-1401	35	18	gradient	gradient	PROPN
ejde-1401	35	19	soliton	soliton	NOUN
ejde-1401	35	20	which	which	PRON
ejde-1401	35	21	admits	admit	VERB
ejde-1401	35	22	a	a	DET
ejde-1401	35	23	concurrent	concurrent	ADJ
ejde-1401	35	24	-	-	PUNCT
ejde-1401	35	25	recurrent	recurrent	NOUN
ejde-1401	35	26	vector	vector	NOUN
ejde-1401	35	27	field	field	NOUN
ejde-1401	35	28	has	have	VERB
ejde-1401	35	29	constant	constant	ADJ
ejde-1401	35	30	scalar	scalar	ADJ
ejde-1401	35	31	curvature	curvature	NOUN
ejde-1401	35	32	equal	equal	ADJ
ejde-1401	35	33	to	to	ADP
ejde-1401	35	34	−n(n−	−n(n−	NOUN
ejde-1401	35	35	1)α2	1)α2	NUM
ejde-1401	35	36	.	.	PUNCT
ejde-1401	36	1	more	more	ADV
ejde-1401	36	2	recently	recently	ADV
ejde-1401	36	3	,	,	PUNCT
ejde-1401	36	4	poddar	poddar	ADJ
ejde-1401	36	5	,	,	PUNCT
ejde-1401	36	6	sharma	sharma	PROPN
ejde-1401	36	7	and	and	CCONJ
ejde-1401	36	8	subramanian	subramanian	PROPN
ejde-1401	37	1	[	[	X
ejde-1401	37	2	22	22	NUM
ejde-1401	37	3	]	]	PUNCT
ejde-1401	37	4	established	establish	VERB
ejde-1401	37	5	the	the	DET
ejde-1401	37	6	concept	concept	NOUN
ejde-1401	37	7	of	of	ADP
ejde-1401	37	8	m	m	NOUN
ejde-1401	37	9	-	-	PUNCT
ejde-1401	37	10	quasi	quasi	ADJ
ejde-1401	37	11	yamabe	yamabe	PROPN
ejde-1401	37	12	gradient	gradient	PROPN
ejde-1401	37	13	soliton	soliton	NOUN
ejde-1401	37	14	.	.	PUNCT
ejde-1401	38	1	more	more	ADV
ejde-1401	38	2	precisely	precisely	ADV
ejde-1401	38	3	,	,	PUNCT
ejde-1401	38	4	let	let	VERB
ejde-1401	38	5	(	(	PUNCT
ejde-1401	38	6	σn	σn	NOUN
ejde-1401	38	7	,	,	PUNCT
ejde-1401	38	8	g	g	NOUN
ejde-1401	38	9	,	,	PUNCT
ejde-1401	38	10	u	u	NOUN
ejde-1401	38	11	)	)	PUNCT
ejde-1401	38	12	be	be	VERB
ejde-1401	38	13	a	a	DET
ejde-1401	38	14	riemannian	riemannian	ADJ
ejde-1401	38	15	manifold	manifold	ADJ
ejde-1401	38	16	σn	σn	NOUN
ejde-1401	38	17	endowed	endow	VERB
ejde-1401	38	18	with	with	ADP
ejde-1401	38	19	the	the	DET
ejde-1401	38	20	metric	metric	ADJ
ejde-1401	38	21	g	g	NOUN
ejde-1401	38	22	and	and	CCONJ
ejde-1401	38	23	a	a	DET
ejde-1401	38	24	smooth	smooth	ADJ
ejde-1401	38	25	function	function	NOUN
ejde-1401	38	26	u	u	NOUN
ejde-1401	38	27	=	=	PUNCT
ejde-1401	38	28	e−	e−	PROPN
ejde-1401	38	29	f	f	PROPN
ejde-1401	38	30	m	m	NOUN
ejde-1401	38	31	∈	∈	PROPN
ejde-1401	38	32	c∞(σn	c∞(σn	NOUN
ejde-1401	38	33	)	)	PUNCT
ejde-1401	38	34	,	,	PUNCT
ejde-1401	38	35	where	where	SCONJ
ejde-1401	38	36	f	f	PROPN
ejde-1401	38	37	∈	∈	PROPN
ejde-1401	38	38	c∞(σn	c∞(σn	NOUN
ejde-1401	38	39	)	)	PUNCT
ejde-1401	38	40	is	be	AUX
ejde-1401	38	41	a	a	DET
ejde-1401	38	42	smooth	smooth	ADJ
ejde-1401	38	43	function	function	NOUN
ejde-1401	38	44	on	on	ADP
ejde-1401	38	45	σn	σn	NOUN
ejde-1401	38	46	and	and	CCONJ
ejde-1401	38	47	0	0	NUM
ejde-1401	38	48	<	<	X
ejde-1401	38	49	m	m	X
ejde-1401	38	50	<	<	X
ejde-1401	38	51	+	+	NOUN
ejde-1401	38	52	∞	∞	PROPN
ejde-1401	38	53	is	be	AUX
ejde-1401	38	54	a	a	DET
ejde-1401	38	55	real	real	ADJ
ejde-1401	38	56	number	number	NOUN
ejde-1401	38	57	.	.	PUNCT
ejde-1401	39	1	since	since	SCONJ
ejde-1401	39	2	∇u	∇u	PROPN
ejde-1401	39	3	=	=	SYM
ejde-1401	39	4	−	−	PROPN
ejde-1401	39	5	u	u	NOUN
ejde-1401	39	6	m∇f	m∇f	NOUN
ejde-1401	39	7	,	,	PUNCT
ejde-1401	39	8	with	with	ADP
ejde-1401	39	9	a	a	DET
ejde-1401	39	10	straightforward	straightforward	ADJ
ejde-1401	39	11	computation	computation	NOUN
ejde-1401	39	12	we	we	PRON
ejde-1401	39	13	obtain	obtain	VERB
ejde-1401	39	14	that	that	PRON
ejde-1401	39	15	∇2u	∇2u	PROPN
ejde-1401	40	1	=	=	SYM
ejde-1401	40	2	u	u	NOUN
ejde-1401	40	3	m2	m2	PROPN
ejde-1401	40	4	∇f	∇f	PROPN
ejde-1401	40	5	⊗∇f	⊗∇f	NOUN
ejde-1401	40	6	−	−	PROPN
ejde-1401	40	7	u	u	NOUN
ejde-1401	40	8	m	m	NOUN
ejde-1401	40	9	∇2f	∇2f	PROPN
ejde-1401	40	10	,	,	PUNCT
ejde-1401	40	11	(	(	PUNCT
ejde-1401	40	12	1.5	1.5	NUM
ejde-1401	40	13	)	)	PUNCT
ejde-1401	40	14	and	and	CCONJ
ejde-1401	40	15	,	,	PUNCT
ejde-1401	40	16	from	from	ADP
ejde-1401	40	17	(	(	PUNCT
ejde-1401	40	18	1.4	1.4	NUM
ejde-1401	40	19	)	)	PUNCT
ejde-1401	40	20	,	,	PUNCT
ejde-1401	40	21	we	we	PRON
ejde-1401	40	22	arrive	arrive	VERB
ejde-1401	40	23	at	at	ADP
ejde-1401	40	24	1	1	NUM
ejde-1401	40	25	2	2	NUM
ejde-1401	40	26	l∇ug	l∇ug	ADJ
ejde-1401	40	27	=	=	SYM
ejde-1401	40	28	−	−	NOUN
ejde-1401	40	29	u	u	NOUN
ejde-1401	40	30	m	m	PROPN
ejde-1401	40	31	(	(	PUNCT
ejde-1401	40	32	r−	r−	PROPN
ejde-1401	40	33	ρ)g	ρ)g	NOUN
ejde-1401	40	34	,	,	PUNCT
ejde-1401	40	35	or	or	CCONJ
ejde-1401	40	36	,	,	PUNCT
ejde-1401	40	37	equivalently	equivalently	ADV
ejde-1401	40	38	,	,	PUNCT
ejde-1401	40	39	∇2u	∇2u	PROPN
ejde-1401	40	40	=	=	SYM
ejde-1401	40	41	−	−	PROPN
ejde-1401	40	42	1	1	NUM
ejde-1401	40	43	m	m	NOUN
ejde-1401	40	44	(	(	PUNCT
ejde-1401	40	45	r−	r−	PROPN
ejde-1401	40	46	ρ)ug	ρ)ug	PROPN
ejde-1401	40	47	.	.	PUNCT
ejde-1401	41	1	(	(	PUNCT
ejde-1401	41	2	1.6	1.6	NUM
ejde-1401	41	3	)	)	PUNCT
ejde-1401	41	4	when	when	SCONJ
ejde-1401	41	5	the	the	DET
ejde-1401	41	6	function	function	NOUN
ejde-1401	41	7	u	u	NOUN
ejde-1401	41	8	is	be	AUX
ejde-1401	41	9	constant	constant	ADJ
ejde-1401	41	10	we	we	PRON
ejde-1401	41	11	say	say	VERB
ejde-1401	41	12	that	that	SCONJ
ejde-1401	41	13	the	the	DET
ejde-1401	41	14	m	m	NOUN
ejde-1401	41	15	-	-	PUNCT
ejde-1401	41	16	quasi	quasi	ADJ
ejde-1401	41	17	yamabe	yamabe	PROPN
ejde-1401	41	18	gradient	gradient	PROPN
ejde-1401	41	19	soliton	soliton	NOUN
ejde-1401	41	20	is	be	AUX
ejde-1401	41	21	trivial	trivial	ADJ
ejde-1401	41	22	.	.	PUNCT
ejde-1401	42	1	in	in	ADP
ejde-1401	42	2	this	this	DET
ejde-1401	42	3	setting	setting	NOUN
ejde-1401	42	4	,	,	PUNCT
ejde-1401	42	5	poddar	poddar	ADJ
ejde-1401	42	6	,	,	PUNCT
ejde-1401	42	7	sharma	sharma	PROPN
ejde-1401	42	8	and	and	CCONJ
ejde-1401	42	9	subramanian	subramanian	PROPN
ejde-1401	43	1	[	[	X
ejde-1401	43	2	22	22	NUM
ejde-1401	43	3	]	]	PUNCT
ejde-1401	43	4	showed	show	VERB
ejde-1401	43	5	that	that	SCONJ
ejde-1401	43	6	every	every	DET
ejde-1401	43	7	compact	compact	ADJ
ejde-1401	43	8	m	m	NOUN
ejde-1401	43	9	-	-	PUNCT
ejde-1401	43	10	quasi	quasi	ADJ
ejde-1401	43	11	yamabe	yamabe	PROPN
ejde-1401	43	12	gradient	gradient	PROPN
ejde-1401	43	13	soliton	soliton	NOUN
ejde-1401	43	14	(	(	PUNCT
ejde-1401	43	15	σn	σn	PROPN
ejde-1401	43	16	,	,	PUNCT
ejde-1401	43	17	g	g	NOUN
ejde-1401	43	18	,	,	PUNCT
ejde-1401	43	19	u	u	NOUN
ejde-1401	43	20	)	)	PUNCT
ejde-1401	43	21	,	,	PUNCT
ejde-1401	43	22	n	n	PROPN
ejde-1401	43	23	>	>	X
ejde-1401	43	24	2	2	NUM
ejde-1401	43	25	,	,	PUNCT
ejde-1401	43	26	has	have	VERB
ejde-1401	43	27	constant	constant	ADJ
ejde-1401	43	28	scalar	scalar	ADJ
ejde-1401	43	29	curvature	curvature	NOUN
ejde-1401	43	30	.	.	PUNCT
ejde-1401	44	1	proceeding	proceed	VERB
ejde-1401	44	2	with	with	ADP
ejde-1401	44	3	this	this	DET
ejde-1401	44	4	picture	picture	NOUN
ejde-1401	44	5	,	,	PUNCT
ejde-1401	44	6	in	in	ADP
ejde-1401	44	7	the	the	DET
ejde-1401	44	8	present	present	ADJ
ejde-1401	44	9	paper	paper	NOUN
ejde-1401	44	10	we	we	PRON
ejde-1401	44	11	extend	extend	VERB
ejde-1401	44	12	the	the	DET
ejde-1401	44	13	techniques	technique	NOUN
ejde-1401	44	14	of	of	ADP
ejde-1401	44	15	[	[	X
ejde-1401	44	16	7	7	X
ejde-1401	44	17	]	]	PUNCT
ejde-1401	44	18	in	in	ADP
ejde-1401	44	19	order	order	NOUN
ejde-1401	44	20	to	to	PART
ejde-1401	44	21	establish	establish	VERB
ejde-1401	44	22	new	new	ADJ
ejde-1401	44	23	characterization	characterization	NOUN
ejde-1401	44	24	and	and	CCONJ
ejde-1401	44	25	nonexistence	nonexistence	NOUN
ejde-1401	44	26	results	result	NOUN
ejde-1401	44	27	concerning	concern	VERB
ejde-1401	44	28	complete	complete	ADJ
ejde-1401	44	29	noncompact	noncompact	NOUN
ejde-1401	44	30	and	and	CCONJ
ejde-1401	44	31	stochastically	stochastically	ADV
ejde-1401	44	32	complete	complete	ADJ
ejde-1401	44	33	m	m	NOUN
ejde-1401	44	34	-	-	PUNCT
ejde-1401	44	35	quasi	quasi	ADJ
ejde-1401	44	36	yamabe	yamabe	PROPN
ejde-1401	44	37	gradient	gradient	PROPN
ejde-1401	44	38	solitons	soliton	NOUN
ejde-1401	44	39	(	(	PUNCT
ejde-1401	44	40	σn	σn	PROPN
ejde-1401	44	41	,	,	PUNCT
ejde-1401	44	42	g	g	NOUN
ejde-1401	44	43	,	,	PUNCT
ejde-1401	44	44	u	u	NOUN
ejde-1401	44	45	)	)	PUNCT
ejde-1401	44	46	through	through	ADP
ejde-1401	44	47	the	the	DET
ejde-1401	44	48	applications	application	NOUN
ejde-1401	44	49	of	of	ADP
ejde-1401	44	50	a	a	DET
ejde-1401	44	51	key	key	ADJ
ejde-1401	44	52	bochner	bochner	NOUN
ejde-1401	44	53	type	type	NOUN
ejde-1401	44	54	formula	formula	NOUN
ejde-1401	44	55	jointly	jointly	ADV
ejde-1401	44	56	with	with	ADP
ejde-1401	44	57	suitable	suitable	ADJ
ejde-1401	44	58	maximum	maximum	ADJ
ejde-1401	44	59	principles	principle	NOUN
ejde-1401	44	60	dealing	deal	VERB
ejde-1401	44	61	,	,	PUNCT
ejde-1401	44	62	in	in	ADP
ejde-1401	44	63	particular	particular	ADJ
ejde-1401	44	64	,	,	PUNCT
ejde-1401	44	65	with	with	ADP
ejde-1401	44	66	the	the	DET
ejde-1401	44	67	notions	notion	NOUN
ejde-1401	44	68	of	of	ADP
ejde-1401	44	69	convergence	convergence	NOUN
ejde-1401	44	70	to	to	ADP
ejde-1401	44	71	zero	zero	NUM
ejde-1401	44	72	at	at	ADP
ejde-1401	44	73	infinity	infinity	NOUN
ejde-1401	44	74	and	and	CCONJ
ejde-1401	44	75	polynomial	polynomial	ADJ
ejde-1401	44	76	and	and	CCONJ
ejde-1401	44	77	exponential	exponential	ADJ
ejde-1401	44	78	volume	volume	NOUN
ejde-1401	44	79	growth	growth	NOUN
ejde-1401	44	80	.	.	PUNCT
ejde-1401	45	1	2	2	X
ejde-1401	45	2	.	.	NOUN
ejde-1401	45	3	suitable	suitable	ADJ
ejde-1401	45	4	bochner	bochner	NOUN
ejde-1401	45	5	type	type	NOUN
ejde-1401	45	6	formula	formula	NOUN
ejde-1401	45	7	in	in	ADP
ejde-1401	45	8	this	this	DET
ejde-1401	45	9	section	section	NOUN
ejde-1401	45	10	,	,	PUNCT
ejde-1401	45	11	we	we	PRON
ejde-1401	45	12	establish	establish	VERB
ejde-1401	45	13	a	a	DET
ejde-1401	45	14	suitable	suitable	ADJ
ejde-1401	45	15	bochner	bochner	NOUN
ejde-1401	45	16	type	type	NOUN
ejde-1401	45	17	formula	formula	NOUN
ejde-1401	45	18	which	which	PRON
ejde-1401	45	19	will	will	AUX
ejde-1401	45	20	be	be	AUX
ejde-1401	45	21	used	use	VERB
ejde-1401	45	22	to	to	PART
ejde-1401	45	23	prove	prove	VERB
ejde-1401	45	24	some	some	PRON
ejde-1401	45	25	of	of	ADP
ejde-1401	45	26	our	our	PRON
ejde-1401	45	27	main	main	ADJ
ejde-1401	45	28	results	result	NOUN
ejde-1401	45	29	.	.	PUNCT
ejde-1401	46	1	we	we	PRON
ejde-1401	46	2	start	start	VERB
ejde-1401	46	3	remembering	remember	VERB
ejde-1401	46	4	the	the	DET
ejde-1401	46	5	classical	classical	ADJ
ejde-1401	46	6	bochner	bochner	NOUN
ejde-1401	46	7	formula	formula	NOUN
ejde-1401	46	8	(	(	PUNCT
ejde-1401	46	9	see	see	VERB
ejde-1401	46	10	for	for	ADP
ejde-1401	46	11	instance	instance	NOUN
ejde-1401	46	12	[	[	X
ejde-1401	46	13	5	5	NUM
ejde-1401	46	14	]	]	SYM
ejde-1401	46	15	):	):	PUNCT
ejde-1401	46	16	1	1	NUM
ejde-1401	46	17	2	2	NUM
ejde-1401	46	18	∆|∇u|2	∆|∇u|2	NOUN
ejde-1401	46	19	=	=	SYM
ejde-1401	46	20	ric(∇u,∇u	ric(∇u,∇u	PROPN
ejde-1401	46	21	)	)	PUNCT
ejde-1401	47	1	+	+	SYM
ejde-1401	47	2	g(∇u,∇∆u	g(∇u,∇∆u	NOUN
ejde-1401	47	3	)	)	PUNCT
ejde-1401	48	1	+	+	PUNCT
ejde-1401	48	2	|∇2u|2	|∇2u|2	NOUN
ejde-1401	48	3	,	,	PUNCT
ejde-1401	48	4	(	(	PUNCT
ejde-1401	48	5	2.1	2.1	NUM
ejde-1401	48	6	)	)	PUNCT
ejde-1401	48	7	where	where	SCONJ
ejde-1401	48	8	ric	ric	PROPN
ejde-1401	48	9	stands	stand	VERB
ejde-1401	48	10	for	for	ADP
ejde-1401	48	11	the	the	DET
ejde-1401	48	12	ricci	ricci	PROPN
ejde-1401	48	13	tensor	tensor	NOUN
ejde-1401	48	14	of	of	ADP
ejde-1401	48	15	(	(	PUNCT
ejde-1401	48	16	σn	σn	PROPN
ejde-1401	48	17	,	,	PUNCT
ejde-1401	48	18	g	g	NOUN
ejde-1401	48	19	)	)	PUNCT
ejde-1401	48	20	.	.	PUNCT
ejde-1401	49	1	on	on	ADP
ejde-1401	49	2	the	the	DET
ejde-1401	49	3	other	other	ADJ
ejde-1401	49	4	hand	hand	NOUN
ejde-1401	49	5	,	,	PUNCT
ejde-1401	49	6	considering	consider	VERB
ejde-1401	49	7	a	a	DET
ejde-1401	49	8	(	(	PUNCT
ejde-1401	49	9	local	local	ADJ
ejde-1401	49	10	)	)	PUNCT
ejde-1401	49	11	orthonormal	orthonormal	ADJ
ejde-1401	49	12	frame	frame	NOUN
ejde-1401	49	13	{	{	PUNCT
ejde-1401	49	14	e1	e1	NOUN
ejde-1401	49	15	,	,	PUNCT
ejde-1401	49	16	·	·	PUNCT
ejde-1401	49	17	·	·	PUNCT
ejde-1401	49	18	·	·	PUNCT
ejde-1401	49	19	,	,	PUNCT
ejde-1401	49	20	en	en	ADP
ejde-1401	49	21	}	}	PUNCT
ejde-1401	49	22	on	on	ADP
ejde-1401	49	23	σn	σn	NOUN
ejde-1401	49	24	,	,	PUNCT
ejde-1401	49	25	from	from	ADP
ejde-1401	49	26	(	(	PUNCT
ejde-1401	49	27	1.6	1.6	NUM
ejde-1401	49	28	)	)	PUNCT
ejde-1401	49	29	we	we	PRON
ejde-1401	49	30	have	have	VERB
ejde-1401	49	31	|∇2u|2	|∇2u|2	NOUN
ejde-1401	49	32	=	=	SYM
ejde-1401	49	33	∑	∑	PUNCT
ejde-1401	49	34	i	i	PRON
ejde-1401	49	35	|∇2u(ei)|2	|∇2u(ei)|2	VERB
ejde-1401	49	36	=	=	PUNCT
ejde-1401	49	37	∑	∑	PUNCT
ejde-1401	49	38	i	i	PRON
ejde-1401	49	39	∣∣	∣∣	NUM
ejde-1401	49	40	1	1	NUM
ejde-1401	49	41	m	m	PROPN
ejde-1401	49	42	(	(	PUNCT
ejde-1401	50	1	r−	r−	PROPN
ejde-1401	50	2	ρ)uei	ρ)uei	PROPN
ejde-1401	50	3	∣∣2	∣∣2	PROPN
ejde-1401	50	4	=	=	SYM
ejde-1401	50	5	n	n	NUM
ejde-1401	50	6	m2	m2	PROPN
ejde-1401	50	7	(	(	PUNCT
ejde-1401	50	8	r−	r−	PROPN
ejde-1401	50	9	ρ)2u2	ρ)2u2	PRON
ejde-1401	50	10	.	.	PUNCT
ejde-1401	51	1	(	(	PUNCT
ejde-1401	51	2	2.2	2.2	NUM
ejde-1401	51	3	)	)	PUNCT
ejde-1401	51	4	ejde-2025/62	ejde-2025/62	NOUN
ejde-1401	51	5	complete	complete	ADJ
ejde-1401	51	6	m	m	NOUN
ejde-1401	51	7	-	-	PUNCT
ejde-1401	51	8	quasi	quasi	ADJ
ejde-1401	51	9	yamabe	yamabe	PROPN
ejde-1401	51	10	gradient	gradient	PROPN
ejde-1401	51	11	solitons	soliton	NOUN
ejde-1401	51	12	3	3	NUM
ejde-1401	51	13	moreover	moreover	ADV
ejde-1401	51	14	,	,	PUNCT
ejde-1401	51	15	choosing	choose	VERB
ejde-1401	51	16	{	{	PUNCT
ejde-1401	51	17	e1	e1	PROPN
ejde-1401	51	18	,	,	PUNCT
ejde-1401	51	19	·	·	PUNCT
ejde-1401	51	20	·	·	PUNCT
ejde-1401	51	21	·	·	PUNCT
ejde-1401	51	22	,	,	PUNCT
ejde-1401	51	23	en	en	X
ejde-1401	51	24	}	}	PUNCT
ejde-1401	51	25	to	to	PART
ejde-1401	51	26	be	be	AUX
ejde-1401	51	27	a	a	DET
ejde-1401	51	28	geodesic	geodesic	ADJ
ejde-1401	51	29	frame	frame	NOUN
ejde-1401	51	30	,	,	PUNCT
ejde-1401	51	31	we	we	PRON
ejde-1401	51	32	claim	claim	VERB
ejde-1401	51	33	that	that	SCONJ
ejde-1401	51	34	ric(∇u,∇u	ric(∇u,∇u	PROPN
ejde-1401	51	35	)	)	PUNCT
ejde-1401	52	1	+	+	SYM
ejde-1401	52	2	g(∇u,∇∆u	g(∇u,∇∆u	NOUN
ejde-1401	52	3	)	)	PUNCT
ejde-1401	52	4	=	=	PUNCT
ejde-1401	53	1	∑	∑	PUNCT
ejde-1401	53	2	i	i	X
ejde-1401	53	3	g(∇ei	g(∇ei	X
ejde-1401	53	4	∇ei	∇ei	PROPN
ejde-1401	53	5	∇u,∇u	∇u,∇u	PROPN
ejde-1401	53	6	)	)	PUNCT
ejde-1401	53	7	.	.	PUNCT
ejde-1401	54	1	(	(	PUNCT
ejde-1401	54	2	2.3	2.3	NUM
ejde-1401	54	3	)	)	PUNCT
ejde-1401	54	4	indeed	indeed	ADV
ejde-1401	54	5	,	,	PUNCT
ejde-1401	54	6	we	we	PRON
ejde-1401	54	7	have	have	VERB
ejde-1401	54	8	that	that	DET
ejde-1401	54	9	ric(∇h,∇h	ric(∇h,∇h	NOUN
ejde-1401	54	10	)	)	PUNCT
ejde-1401	55	1	=	=	PUNCT
ejde-1401	55	2	∑	∑	PUNCT
ejde-1401	55	3	i	i	PROPN
ejde-1401	55	4	g(r(∇h	g(r(∇h	PROPN
ejde-1401	55	5	,	,	PUNCT
ejde-1401	55	6	ei)∇h	ei)∇h	NOUN
ejde-1401	55	7	,	,	PUNCT
ejde-1401	55	8	ei	ei	NOUN
ejde-1401	55	9	)	)	PUNCT
ejde-1401	55	10	=	=	PUNCT
ejde-1401	56	1	∑	∑	PUNCT
ejde-1401	56	2	i	i	PRON
ejde-1401	56	3	g(∇ei	g(∇ei	VERB
ejde-1401	56	4	∇∇h∇h−∇∇h∇ei	∇∇h∇h−∇∇h∇ei	PROPN
ejde-1401	56	5	∇h+∇[∇h	∇h+∇[∇h	PROPN
ejde-1401	56	6	,	,	PUNCT
ejde-1401	56	7	ei]∇h	ei]∇h	PROPN
ejde-1401	56	8	,	,	PUNCT
ejde-1401	56	9	ei	ei	NOUN
ejde-1401	56	10	)	)	PUNCT
ejde-1401	56	11	.	.	PUNCT
ejde-1401	57	1	(	(	PUNCT
ejde-1401	57	2	2.4	2.4	NUM
ejde-1401	57	3	)	)	PUNCT
ejde-1401	57	4	but	but	CCONJ
ejde-1401	57	5	,	,	PUNCT
ejde-1401	57	6	since	since	SCONJ
ejde-1401	57	7	{	{	PUNCT
ejde-1401	57	8	e1	e1	PROPN
ejde-1401	57	9	,	,	PUNCT
ejde-1401	57	10	·	·	PUNCT
ejde-1401	57	11	·	·	PUNCT
ejde-1401	57	12	·	·	PUNCT
ejde-1401	57	13	,	,	PUNCT
ejde-1401	57	14	en	en	ADP
ejde-1401	57	15	}	}	PUNCT
ejde-1401	57	16	is	be	AUX
ejde-1401	57	17	a	a	DET
ejde-1401	57	18	geodesic	geodesic	ADJ
ejde-1401	57	19	frame	frame	NOUN
ejde-1401	57	20	,	,	PUNCT
ejde-1401	57	21	we	we	PRON
ejde-1401	57	22	obtain∑	obtain∑	VERB
ejde-1401	57	23	i	i	PRON
ejde-1401	57	24	g(∇∇h∇ei	g(∇∇h∇ei	VERB
ejde-1401	58	1	∇h	∇h	NOUN
ejde-1401	58	2	,	,	PUNCT
ejde-1401	58	3	ei	ei	NOUN
ejde-1401	58	4	)	)	PUNCT
ejde-1401	58	5	=	=	PUNCT
ejde-1401	59	1	∑	∑	PUNCT
ejde-1401	59	2	i	i	PRON
ejde-1401	59	3	∇h(g(∇ei	∇h(g(∇ei	PROPN
ejde-1401	59	4	∇h	∇h	PROPN
ejde-1401	59	5	,	,	PUNCT
ejde-1401	59	6	ei	ei	NOUN
ejde-1401	59	7	)	)	PUNCT
ejde-1401	59	8	)	)	PUNCT
ejde-1401	60	1	=	=	PUNCT
ejde-1401	60	2	∇h(∆h	∇h(∆h	NOUN
ejde-1401	60	3	)	)	PUNCT
ejde-1401	60	4	=	=	VERB
ejde-1401	60	5	g(∇h,∇∆h	g(∇h,∇∆h	ADJ
ejde-1401	60	6	)	)	PUNCT
ejde-1401	60	7	.	.	PUNCT
ejde-1401	61	1	(	(	PUNCT
ejde-1401	61	2	2.5	2.5	NUM
ejde-1401	61	3	)	)	PUNCT
ejde-1401	61	4	moreover	moreover	ADV
ejde-1401	61	5	,	,	PUNCT
ejde-1401	61	6	we	we	PRON
ejde-1401	61	7	also	also	ADV
ejde-1401	61	8	obtain	obtain	VERB
ejde-1401	61	9	g(∇ei∇∇h∇h+∇[∇h	g(∇ei∇∇h∇h+∇[∇h	ADJ
ejde-1401	61	10	,	,	PUNCT
ejde-1401	61	11	ei]∇h	ei]∇h	PROPN
ejde-1401	61	12	,	,	PUNCT
ejde-1401	61	13	ei	ei	NOUN
ejde-1401	61	14	)	)	PUNCT
ejde-1401	61	15	=	=	SYM
ejde-1401	61	16	ei(g(∇∇h∇h	ei(g(∇∇h∇h	PROPN
ejde-1401	61	17	,	,	PUNCT
ejde-1401	61	18	ei))−	ei))−	NOUN
ejde-1401	61	19	g(∇∇h∇h,∇ei	g(∇∇h∇h,∇ei	NOUN
ejde-1401	61	20	ei)−	ei)−	NOUN
ejde-1401	61	21	g(∇ei	g(∇ei	ADP
ejde-1401	61	22	∇h	∇h	PROPN
ejde-1401	61	23	,	,	PUNCT
ejde-1401	61	24	[	[	X
ejde-1401	61	25	ei,∇h	ei,∇h	NOUN
ejde-1401	61	26	]	]	X
ejde-1401	61	27	)	)	PUNCT
ejde-1401	62	1	=	=	SYM
ejde-1401	62	2	ei(g(∇ei	ei(g(∇ei	PROPN
ejde-1401	62	3	∇h,∇h))−	∇h,∇h))−	PROPN
ejde-1401	62	4	g(∇ei	g(∇ei	X
ejde-1401	62	5	∇h,∇ei	∇h,∇ei	PROPN
ejde-1401	62	6	∇h−∇∇hei	∇h−∇∇hei	PROPN
ejde-1401	62	7	)	)	PUNCT
ejde-1401	62	8	=	=	PROPN
ejde-1401	62	9	g(∇ei	g(∇ei	X
ejde-1401	62	10	∇ei	∇ei	PROPN
ejde-1401	62	11	∇h,∇h	∇h,∇h	PROPN
ejde-1401	62	12	)	)	PUNCT
ejde-1401	62	13	.	.	PUNCT
ejde-1401	63	1	(	(	PUNCT
ejde-1401	63	2	2.6	2.6	NUM
ejde-1401	63	3	)	)	PUNCT
ejde-1401	63	4	hence	hence	ADV
ejde-1401	63	5	,	,	PUNCT
ejde-1401	63	6	inserting	insert	VERB
ejde-1401	63	7	(	(	PUNCT
ejde-1401	63	8	2.5	2.5	NUM
ejde-1401	63	9	)	)	PUNCT
ejde-1401	63	10	and	and	CCONJ
ejde-1401	63	11	(	(	PUNCT
ejde-1401	63	12	2.6	2.6	NUM
ejde-1401	63	13	)	)	PUNCT
ejde-1401	63	14	into	into	ADP
ejde-1401	63	15	(	(	PUNCT
ejde-1401	63	16	2.4	2.4	NUM
ejde-1401	63	17	)	)	PUNCT
ejde-1401	63	18	we	we	PRON
ejde-1401	63	19	arrive	arrive	VERB
ejde-1401	63	20	at	at	ADP
ejde-1401	63	21	(	(	PUNCT
ejde-1401	63	22	2.3	2.3	NUM
ejde-1401	63	23	)	)	PUNCT
ejde-1401	63	24	.	.	PUNCT
ejde-1401	64	1	thus	thus	ADV
ejde-1401	64	2	,	,	PUNCT
ejde-1401	64	3	from	from	ADP
ejde-1401	64	4	(	(	PUNCT
ejde-1401	64	5	1.6	1.6	NUM
ejde-1401	64	6	)	)	PUNCT
ejde-1401	64	7	and	and	CCONJ
ejde-1401	64	8	(	(	PUNCT
ejde-1401	64	9	2.3	2.3	NUM
ejde-1401	64	10	)	)	PUNCT
ejde-1401	64	11	we	we	PRON
ejde-1401	64	12	obtain	obtain	VERB
ejde-1401	64	13	ric(∇u,∇u	ric(∇u,∇u	NOUN
ejde-1401	64	14	)	)	PUNCT
ejde-1401	65	1	+	+	SYM
ejde-1401	65	2	g(∇u,∇∆u	g(∇u,∇∆u	NOUN
ejde-1401	65	3	)	)	PUNCT
ejde-1401	65	4	=	=	SYM
ejde-1401	66	1	−	−	PROPN
ejde-1401	66	2	1	1	NUM
ejde-1401	66	3	m	m	NOUN
ejde-1401	66	4	g(∇((r−	g(∇((r−	NOUN
ejde-1401	66	5	ρ)u),∇u	ρ)u),∇u	NOUN
ejde-1401	66	6	)	)	PUNCT
ejde-1401	66	7	.	.	PUNCT
ejde-1401	67	1	(	(	PUNCT
ejde-1401	67	2	2.7	2.7	NUM
ejde-1401	67	3	)	)	PUNCT
ejde-1401	67	4	but	but	CCONJ
ejde-1401	67	5	,	,	PUNCT
ejde-1401	67	6	taking	take	VERB
ejde-1401	67	7	the	the	DET
ejde-1401	67	8	trace	trace	NOUN
ejde-1401	67	9	in	in	ADP
ejde-1401	67	10	(	(	PUNCT
ejde-1401	67	11	1.6	1.6	NUM
ejde-1401	67	12	)	)	PUNCT
ejde-1401	67	13	we	we	PRON
ejde-1401	67	14	obtain	obtain	VERB
ejde-1401	67	15	∆u	∆u	ADV
ejde-1401	67	16	=	=	SYM
ejde-1401	67	17	−	−	PROPN
ejde-1401	67	18	n	n	VERB
ejde-1401	67	19	m	m	PROPN
ejde-1401	67	20	(	(	PUNCT
ejde-1401	67	21	r−	r−	PROPN
ejde-1401	67	22	ρ)u	ρ)u	PROPN
ejde-1401	67	23	.	.	PUNCT
ejde-1401	68	1	(	(	PUNCT
ejde-1401	68	2	2.8	2.8	NUM
ejde-1401	68	3	)	)	PUNCT
ejde-1401	68	4	consequently	consequently	ADV
ejde-1401	68	5	,	,	PUNCT
ejde-1401	68	6	from	from	ADP
ejde-1401	68	7	(	(	PUNCT
ejde-1401	68	8	2.8	2.8	NUM
ejde-1401	68	9	)	)	PUNCT
ejde-1401	68	10	we	we	PRON
ejde-1401	68	11	have	have	AUX
ejde-1401	68	12	g(∇u,∇∆u	g(∇u,∇∆u	VERB
ejde-1401	68	13	)	)	PUNCT
ejde-1401	68	14	=	=	SYM
ejde-1401	69	1	−	−	PROPN
ejde-1401	69	2	n	n	CCONJ
ejde-1401	69	3	m	m	PROPN
ejde-1401	69	4	g(∇((r−	g(∇((r−	ADJ
ejde-1401	69	5	ρ)u),∇u	ρ)u),∇u	NOUN
ejde-1401	69	6	)	)	PUNCT
ejde-1401	69	7	.	.	PUNCT
ejde-1401	70	1	so	so	ADV
ejde-1401	70	2	,	,	PUNCT
ejde-1401	70	3	we	we	PRON
ejde-1401	70	4	conclude	conclude	VERB
ejde-1401	70	5	that	that	SCONJ
ejde-1401	70	6	−	−	PROPN
ejde-1401	70	7	1	1	NUM
ejde-1401	70	8	m	m	NOUN
ejde-1401	70	9	g(∇((r−	g(∇((r−	NOUN
ejde-1401	70	10	ρ)u),∇u	ρ)u),∇u	NOUN
ejde-1401	70	11	)	)	PUNCT
ejde-1401	71	1	=	=	PUNCT
ejde-1401	72	1	−	−	PROPN
ejde-1401	72	2	1	1	NUM
ejde-1401	72	3	(	(	PUNCT
ejde-1401	72	4	n−	n−	NOUN
ejde-1401	72	5	1	1	NUM
ejde-1401	72	6	)	)	PUNCT
ejde-1401	72	7	ric(∇u,∇u	ric(∇u,∇u	NOUN
ejde-1401	72	8	)	)	PUNCT
ejde-1401	72	9	.	.	PUNCT
ejde-1401	73	1	(	(	PUNCT
ejde-1401	73	2	2.9	2.9	NUM
ejde-1401	73	3	)	)	PUNCT
ejde-1401	73	4	hence	hence	ADV
ejde-1401	73	5	,	,	PUNCT
ejde-1401	73	6	from	from	ADP
ejde-1401	73	7	(	(	PUNCT
ejde-1401	73	8	2.1	2.1	NUM
ejde-1401	73	9	)	)	PUNCT
ejde-1401	73	10	,	,	PUNCT
ejde-1401	73	11	(	(	PUNCT
ejde-1401	73	12	2.7	2.7	NUM
ejde-1401	73	13	)	)	PUNCT
ejde-1401	73	14	and	and	CCONJ
ejde-1401	73	15	(	(	PUNCT
ejde-1401	73	16	2.9	2.9	NUM
ejde-1401	73	17	)	)	PUNCT
ejde-1401	73	18	we	we	PRON
ejde-1401	73	19	reach	reach	VERB
ejde-1401	73	20	our	our	PRON
ejde-1401	73	21	suitable	suitable	ADJ
ejde-1401	73	22	bochner	bochner	NOUN
ejde-1401	73	23	type	type	NOUN
ejde-1401	73	24	formula	formula	NOUN
ejde-1401	73	25	1	1	NUM
ejde-1401	73	26	2	2	NUM
ejde-1401	73	27	∆|∇u|2	∆|∇u|2	NOUN
ejde-1401	73	28	=	=	SYM
ejde-1401	73	29	|∇2u|2	|∇2u|2	PROPN
ejde-1401	73	30	−	−	NUM
ejde-1401	73	31	1	1	NUM
ejde-1401	73	32	n−	n−	NOUN
ejde-1401	73	33	1	1	NUM
ejde-1401	73	34	ric(∇u,∇u	ric(∇u,∇u	NOUN
ejde-1401	73	35	)	)	PUNCT
ejde-1401	73	36	.	.	PUNCT
ejde-1401	74	1	(	(	PUNCT
ejde-1401	74	2	2.10	2.10	NUM
ejde-1401	74	3	)	)	PUNCT
ejde-1401	74	4	3	3	NUM
ejde-1401	74	5	.	.	X
ejde-1401	74	6	main	main	ADJ
ejde-1401	74	7	results	result	NOUN
ejde-1401	74	8	this	this	DET
ejde-1401	74	9	section	section	NOUN
ejde-1401	74	10	is	be	AUX
ejde-1401	74	11	devoted	devote	VERB
ejde-1401	74	12	to	to	PART
ejde-1401	74	13	establish	establish	VERB
ejde-1401	74	14	our	our	PRON
ejde-1401	74	15	characterization	characterization	NOUN
ejde-1401	74	16	and	and	CCONJ
ejde-1401	74	17	nonexistence	nonexistence	NOUN
ejde-1401	74	18	results	result	NOUN
ejde-1401	74	19	concerning	concern	VERB
ejde-1401	74	20	complete	complete	ADJ
ejde-1401	74	21	noncompact	noncompact	NOUN
ejde-1401	74	22	and	and	CCONJ
ejde-1401	74	23	stochastically	stochastically	ADV
ejde-1401	74	24	complete	complete	ADJ
ejde-1401	74	25	m	m	NOUN
ejde-1401	74	26	-	-	PUNCT
ejde-1401	74	27	quasi	quasi	ADJ
ejde-1401	74	28	yamabe	yamabe	ADJ
ejde-1401	74	29	gradient	gradient	NOUN
ejde-1401	74	30	solitons	soliton	NOUN
ejde-1401	74	31	.	.	PUNCT
ejde-1401	75	1	for	for	ADP
ejde-1401	75	2	this	this	PRON
ejde-1401	75	3	,	,	PUNCT
ejde-1401	75	4	we	we	PRON
ejde-1401	75	5	will	will	AUX
ejde-1401	75	6	apply	apply	VERB
ejde-1401	75	7	suitable	suitable	ADJ
ejde-1401	75	8	maximum	maximum	ADJ
ejde-1401	75	9	principles	principle	NOUN
ejde-1401	75	10	as	as	ADP
ejde-1401	75	11	main	main	ADJ
ejde-1401	75	12	analytical	analytical	ADJ
ejde-1401	75	13	tools	tool	NOUN
ejde-1401	75	14	.	.	PUNCT
ejde-1401	76	1	3.1	3.1	NUM
ejde-1401	76	2	.	.	PUNCT
ejde-1401	77	1	via	via	ADP
ejde-1401	77	2	integrability	integrability	NOUN
ejde-1401	77	3	conditions	condition	NOUN
ejde-1401	77	4	.	.	PUNCT
ejde-1401	78	1	yau	yau	PRON
ejde-1401	79	1	[	[	X
ejde-1401	79	2	28	28	NUM
ejde-1401	79	3	]	]	X
ejde-1401	79	4	generalizing	generalize	VERB
ejde-1401	79	5	a	a	DET
ejde-1401	79	6	previous	previous	ADJ
ejde-1401	79	7	result	result	NOUN
ejde-1401	79	8	due	due	ADP
ejde-1401	79	9	to	to	ADP
ejde-1401	79	10	gaffney	gaffney	NOUN
ejde-1401	79	11	[	[	X
ejde-1401	79	12	9	9	NUM
ejde-1401	79	13	]	]	PUNCT
ejde-1401	79	14	,	,	PUNCT
ejde-1401	79	15	established	establish	VERB
ejde-1401	79	16	the	the	DET
ejde-1401	79	17	following	follow	VERB
ejde-1401	79	18	version	version	NOUN
ejde-1401	79	19	of	of	ADP
ejde-1401	79	20	stokes	stokes	PROPN
ejde-1401	79	21	’	'	PUNCT
ejde-1401	79	22	theorem	theorem	VERB
ejde-1401	79	23	on	on	ADP
ejde-1401	79	24	an	an	DET
ejde-1401	79	25	n	n	ADV
ejde-1401	79	26	-	-	PUNCT
ejde-1401	79	27	dimensional	dimensional	ADJ
ejde-1401	79	28	complete	complete	ADJ
ejde-1401	79	29	noncompact	noncompact	NOUN
ejde-1401	79	30	riemannian	riemannian	NOUN
ejde-1401	79	31	manifold	manifold	ADJ
ejde-1401	79	32	σn	σn	NOUN
ejde-1401	79	33	:	:	PUNCT
ejde-1401	79	34	if	if	SCONJ
ejde-1401	79	35	ω	ω	PROPN
ejde-1401	79	36	∈	∈	PROPN
ejde-1401	79	37	ωn−1(σn	ωn−1(σn	NOUN
ejde-1401	79	38	)	)	PUNCT
ejde-1401	79	39	is	be	AUX
ejde-1401	79	40	an	an	DET
ejde-1401	79	41	integrable	integrable	ADJ
ejde-1401	79	42	(	(	PUNCT
ejde-1401	79	43	n−	n−	NOUN
ejde-1401	79	44	1)-differential	1)-differential	PROPN
ejde-1401	79	45	form	form	NOUN
ejde-1401	79	46	on	on	ADP
ejde-1401	79	47	σn	σn	NOUN
ejde-1401	79	48	,	,	PUNCT
ejde-1401	79	49	then	then	ADV
ejde-1401	79	50	there	there	PRON
ejde-1401	79	51	exists	exist	VERB
ejde-1401	79	52	a	a	DET
ejde-1401	79	53	sequence	sequence	NOUN
ejde-1401	79	54	bi	bi	NOUN
ejde-1401	79	55	of	of	ADP
ejde-1401	79	56	domains	domain	NOUN
ejde-1401	79	57	on	on	ADP
ejde-1401	79	58	σn	σn	PRON
ejde-1401	79	59	such	such	ADJ
ejde-1401	79	60	that	that	SCONJ
ejde-1401	79	61	bi	bi	PROPN
ejde-1401	79	62	⊂	⊂	PROPN
ejde-1401	79	63	bi+1	bi+1	PROPN
ejde-1401	79	64	,	,	PUNCT
ejde-1401	79	65	σn	σn	X
ejde-1401	79	66	=	=	PUNCT
ejde-1401	79	67	∪i≥1bi	∪i≥1bi	NOUN
ejde-1401	79	68	and	and	CCONJ
ejde-1401	79	69	lim	lim	PROPN
ejde-1401	79	70	i→+∞	i→+∞	PROPN
ejde-1401	79	71	∫	∫	PROPN
ejde-1401	79	72	bi	bi	NOUN
ejde-1401	79	73	dω	dω	PROPN
ejde-1401	79	74	=	=	NOUN
ejde-1401	80	1	0	0	X
ejde-1401	80	2	.	.	PUNCT
ejde-1401	80	3	suppose	suppose	VERB
ejde-1401	80	4	σn	σn	PROPN
ejde-1401	80	5	is	be	AUX
ejde-1401	80	6	oriented	orient	VERB
ejde-1401	80	7	by	by	ADP
ejde-1401	80	8	the	the	DET
ejde-1401	80	9	volume	volume	NOUN
ejde-1401	80	10	element	element	NOUN
ejde-1401	80	11	dς	dς	PROPN
ejde-1401	80	12	,	,	PUNCT
ejde-1401	80	13	and	and	CCONJ
ejde-1401	80	14	let	let	VERB
ejde-1401	80	15	lq(σn	lq(σn	NOUN
ejde-1401	80	16	)	)	PUNCT
ejde-1401	80	17	be	be	AUX
ejde-1401	80	18	the	the	DET
ejde-1401	80	19	space	space	NOUN
ejde-1401	80	20	of	of	ADP
ejde-1401	80	21	lebesgue	lebesgue	ADJ
ejde-1401	80	22	q	q	ADJ
ejde-1401	80	23	-	-	PUNCT
ejde-1401	80	24	integrable	integrable	ADJ
ejde-1401	80	25	functions	function	NOUN
ejde-1401	80	26	on	on	ADP
ejde-1401	80	27	σn	σn	NOUN
ejde-1401	80	28	,	,	PUNCT
ejde-1401	80	29	that	that	PRON
ejde-1401	80	30	means	mean	VERB
ejde-1401	80	31	lq(σn	lq(σn	NOUN
ejde-1401	80	32	)	)	PUNCT
ejde-1401	80	33	:	:	PUNCT
ejde-1401	81	1	=	=	SYM
ejde-1401	81	2	{	{	PUNCT
ejde-1401	81	3	u	u	NOUN
ejde-1401	81	4	∈	∈	PROPN
ejde-1401	81	5	c∞(σn	c∞(σn	NOUN
ejde-1401	81	6	)	)	PUNCT
ejde-1401	81	7	;	;	PUNCT
ejde-1401	82	1	∫	∫	PROPN
ejde-1401	82	2	σ	σ	PROPN
ejde-1401	82	3	|u|qdς	|u|qdς	PUNCT
ejde-1401	82	4	<	<	X
ejde-1401	82	5	+	+	PROPN
ejde-1401	82	6	∞	∞	PROPN
ejde-1401	82	7	,	,	PUNCT
ejde-1401	82	8	1	1	NUM
ejde-1401	82	9	≤	≤	NOUN
ejde-1401	82	10	q	q	NOUN
ejde-1401	82	11	<	<	X
ejde-1401	82	12	+	+	NOUN
ejde-1401	82	13	∞	∞	NUM
ejde-1401	82	14	}	}	PUNCT
ejde-1401	82	15	.	.	PUNCT
ejde-1401	83	1	4	4	NUM
ejde-1401	83	2	g.	g.	PROPN
ejde-1401	83	3	molica	molica	PROPN
ejde-1401	83	4	bisci	bisci	PROPN
ejde-1401	83	5	,	,	PUNCT
ejde-1401	83	6	h.	h.	PROPN
ejde-1401	83	7	f.	f.	PROPN
ejde-1401	83	8	de	de	PROPN
ejde-1401	83	9	lima	lima	PROPN
ejde-1401	83	10	,	,	PUNCT
ejde-1401	83	11	a.	a.	PROPN
ejde-1401	83	12	v.	v.	PROPN
ejde-1401	83	13	f.	f.	PROPN
ejde-1401	83	14	leite	leite	PROPN
ejde-1401	83	15	,	,	PUNCT
ejde-1401	83	16	m.	m.	NOUN
ejde-1401	83	17	a.	a.	PROPN
ejde-1401	83	18	l.	l.	PROPN
ejde-1401	83	19	velásquez	velásquez	PROPN
ejde-1401	83	20	ejde-2025/62	ejde-2025/62	PROPN
ejde-1401	83	21	if	if	SCONJ
ejde-1401	83	22	ω	ω	NUM
ejde-1401	83	23	=	=	PUNCT
ejde-1401	83	24	ιxdς	ιxdς	PROPN
ejde-1401	83	25	is	be	AUX
ejde-1401	83	26	the	the	DET
ejde-1401	83	27	contraction	contraction	NOUN
ejde-1401	83	28	of	of	ADP
ejde-1401	83	29	dς	dς	NOUN
ejde-1401	83	30	in	in	ADP
ejde-1401	83	31	the	the	DET
ejde-1401	83	32	direction	direction	NOUN
ejde-1401	83	33	of	of	ADP
ejde-1401	83	34	a	a	DET
ejde-1401	83	35	smooth	smooth	ADJ
ejde-1401	83	36	vector	vector	NOUN
ejde-1401	83	37	field	field	NOUN
ejde-1401	83	38	x	x	PUNCT
ejde-1401	83	39	on	on	ADP
ejde-1401	83	40	σn	σn	NOUN
ejde-1401	83	41	,	,	PUNCT
ejde-1401	83	42	then	then	ADV
ejde-1401	83	43	caminha	caminha	NOUN
ejde-1401	83	44	obtained	obtain	VERB
ejde-1401	83	45	the	the	DET
ejde-1401	83	46	following	following	ADJ
ejde-1401	83	47	consequence	consequence	NOUN
ejde-1401	83	48	of	of	ADP
ejde-1401	83	49	yau	yau	PROPN
ejde-1401	83	50	’s	’s	PART
ejde-1401	83	51	result	result	NOUN
ejde-1401	83	52	(	(	PUNCT
ejde-1401	83	53	see	see	VERB
ejde-1401	83	54	[	[	X
ejde-1401	83	55	6	6	NUM
ejde-1401	83	56	,	,	PUNCT
ejde-1401	83	57	proposition	proposition	NOUN
ejde-1401	83	58	2.1	2.1	NUM
ejde-1401	83	59	]	]	PUNCT
ejde-1401	83	60	)	)	PUNCT
ejde-1401	83	61	.	.	PUNCT
ejde-1401	84	1	lemma	lemma	PROPN
ejde-1401	84	2	3.1	3.1	NUM
ejde-1401	84	3	.	.	PUNCT
ejde-1401	85	1	let	let	VERB
ejde-1401	85	2	x	x	PRON
ejde-1401	85	3	be	be	AUX
ejde-1401	85	4	a	a	DET
ejde-1401	85	5	smooth	smooth	ADJ
ejde-1401	85	6	vector	vector	NOUN
ejde-1401	85	7	field	field	NOUN
ejde-1401	85	8	on	on	ADP
ejde-1401	85	9	the	the	DET
ejde-1401	85	10	n	n	ADV
ejde-1401	85	11	-	-	PUNCT
ejde-1401	85	12	dimensional	dimensional	ADJ
ejde-1401	85	13	complete	complete	ADJ
ejde-1401	85	14	noncompact	noncompact	NOUN
ejde-1401	85	15	oriented	orient	VERB
ejde-1401	85	16	riemannian	riemannian	ADJ
ejde-1401	85	17	manifold	manifold	NOUN
ejde-1401	85	18	(	(	PUNCT
ejde-1401	85	19	σn	σn	PROPN
ejde-1401	85	20	,	,	PUNCT
ejde-1401	85	21	g	g	NOUN
ejde-1401	85	22	)	)	PUNCT
ejde-1401	85	23	,	,	PUNCT
ejde-1401	85	24	such	such	ADJ
ejde-1401	85	25	that	that	SCONJ
ejde-1401	85	26	divg	divg	NOUN
ejde-1401	85	27	x	x	PUNCT
ejde-1401	85	28	does	do	AUX
ejde-1401	85	29	not	not	PART
ejde-1401	85	30	change	change	VERB
ejde-1401	85	31	sign	sign	NOUN
ejde-1401	85	32	on	on	ADP
ejde-1401	85	33	(	(	PUNCT
ejde-1401	85	34	σn	σn	NOUN
ejde-1401	85	35	,	,	PUNCT
ejde-1401	85	36	g	g	NOUN
ejde-1401	85	37	)	)	PUNCT
ejde-1401	85	38	.	.	PUNCT
ejde-1401	86	1	if	if	SCONJ
ejde-1401	86	2	|x|	|x|	PROPN
ejde-1401	86	3	∈	∈	PROPN
ejde-1401	86	4	l1(σn	l1(σn	PROPN
ejde-1401	86	5	)	)	PUNCT
ejde-1401	86	6	,	,	PUNCT
ejde-1401	86	7	then	then	ADV
ejde-1401	86	8	divg	divg	VERB
ejde-1401	86	9	x	x	PUNCT
ejde-1401	86	10	=	=	PUNCT
ejde-1401	86	11	0	0	X
ejde-1401	86	12	.	.	PUNCT
ejde-1401	87	1	now	now	ADV
ejde-1401	87	2	,	,	PUNCT
ejde-1401	87	3	we	we	PRON
ejde-1401	87	4	are	be	AUX
ejde-1401	87	5	in	in	ADP
ejde-1401	87	6	a	a	DET
ejde-1401	87	7	position	position	NOUN
ejde-1401	87	8	to	to	PART
ejde-1401	87	9	present	present	VERB
ejde-1401	87	10	our	our	PRON
ejde-1401	87	11	first	first	ADJ
ejde-1401	87	12	characterization	characterization	NOUN
ejde-1401	87	13	result	result	NOUN
ejde-1401	87	14	related	relate	VERB
ejde-1401	87	15	to	to	PART
ejde-1401	87	16	complete	complete	VERB
ejde-1401	87	17	noncompact	noncompact	NOUN
ejde-1401	87	18	m	m	NOUN
ejde-1401	87	19	-	-	PUNCT
ejde-1401	87	20	quasi	quasi	ADJ
ejde-1401	87	21	yamabe	yamabe	PROPN
ejde-1401	87	22	gradient	gradient	PROPN
ejde-1401	87	23	soliton	soliton	NOUN
ejde-1401	87	24	.	.	PUNCT
ejde-1401	88	1	theorem	theorem	ADJ
ejde-1401	88	2	3.2	3.2	NUM
ejde-1401	88	3	.	.	PUNCT
ejde-1401	89	1	let	let	AUX
ejde-1401	89	2	(	(	PUNCT
ejde-1401	89	3	σn	σn	NOUN
ejde-1401	89	4	,	,	PUNCT
ejde-1401	89	5	g	g	NOUN
ejde-1401	89	6	,	,	PUNCT
ejde-1401	89	7	u	u	NOUN
ejde-1401	89	8	)	)	PUNCT
ejde-1401	89	9	be	be	AUX
ejde-1401	89	10	a	a	DET
ejde-1401	89	11	complete	complete	ADJ
ejde-1401	89	12	noncompact	noncompact	NOUN
ejde-1401	89	13	m	m	NOUN
ejde-1401	89	14	-	-	PUNCT
ejde-1401	89	15	quasi	quasi	ADJ
ejde-1401	89	16	yamabe	yamabe	PROPN
ejde-1401	89	17	gradient	gradient	PROPN
ejde-1401	89	18	soliton	soliton	NOUN
ejde-1401	89	19	whose	whose	DET
ejde-1401	89	20	ricci	ricci	PROPN
ejde-1401	89	21	tensor	tensor	NOUN
ejde-1401	89	22	satisfies	satisfie	NOUN
ejde-1401	89	23	ric(∇u,∇u	ric(∇u,∇u	PROPN
ejde-1401	89	24	)	)	PUNCT
ejde-1401	89	25	≤	≤	NOUN
ejde-1401	89	26	0	0	NUM
ejde-1401	90	1	and	and	CCONJ
ejde-1401	90	2	such	such	ADJ
ejde-1401	90	3	that	that	SCONJ
ejde-1401	90	4	|∇|∇u|2|	|∇|∇u|2|	PROPN
ejde-1401	90	5	∈	∈	PROPN
ejde-1401	90	6	l1(σn	l1(σn	PROPN
ejde-1401	90	7	)	)	PUNCT
ejde-1401	90	8	,	,	PUNCT
ejde-1401	90	9	then	then	ADV
ejde-1401	90	10	r	r	NOUN
ejde-1401	90	11	=	=	SYM
ejde-1401	90	12	ρ	ρ	PROPN
ejde-1401	90	13	on	on	ADP
ejde-1401	90	14	σn	σn	PROPN
ejde-1401	90	15	.	.	PUNCT
ejde-1401	90	16	proof	proof	NOUN
ejde-1401	90	17	.	.	PUNCT
ejde-1401	91	1	let	let	VERB
ejde-1401	91	2	us	we	PRON
ejde-1401	91	3	take	take	VERB
ejde-1401	91	4	the	the	DET
ejde-1401	91	5	smooth	smooth	ADJ
ejde-1401	91	6	vector	vector	NOUN
ejde-1401	91	7	field	field	NOUN
ejde-1401	91	8	x	x	PUNCT
ejde-1401	91	9	=	=	PUNCT
ejde-1401	91	10	∇|∇u|2	∇|∇u|2	PROPN
ejde-1401	91	11	∈	∈	PROPN
ejde-1401	91	12	x(σn	x(σn	PROPN
ejde-1401	91	13	)	)	PUNCT
ejde-1401	91	14	.	.	PUNCT
ejde-1401	92	1	in	in	ADP
ejde-1401	92	2	this	this	DET
ejde-1401	92	3	setting	setting	NOUN
ejde-1401	92	4	,	,	PUNCT
ejde-1401	92	5	by	by	ADP
ejde-1401	92	6	hypothesis	hypothesis	NOUN
ejde-1401	92	7	,	,	PUNCT
ejde-1401	92	8	we	we	PRON
ejde-1401	92	9	have	have	VERB
ejde-1401	92	10	that	that	DET
ejde-1401	92	11	|x|	|x|	PROPN
ejde-1401	92	12	∈	∈	PROPN
ejde-1401	92	13	l1(σn	l1(σn	PROPN
ejde-1401	92	14	)	)	PUNCT
ejde-1401	92	15	.	.	PUNCT
ejde-1401	93	1	moreover	moreover	ADV
ejde-1401	93	2	,	,	PUNCT
ejde-1401	93	3	taking	take	VERB
ejde-1401	93	4	into	into	ADP
ejde-1401	93	5	account	account	NOUN
ejde-1401	93	6	that	that	SCONJ
ejde-1401	93	7	ric(∇u,∇u	ric(∇u,∇u	NOUN
ejde-1401	93	8	)	)	PUNCT
ejde-1401	93	9	≤	≤	NOUN
ejde-1401	93	10	0	0	NUM
ejde-1401	93	11	,	,	PUNCT
ejde-1401	93	12	from	from	ADP
ejde-1401	93	13	(	(	PUNCT
ejde-1401	93	14	2.10	2.10	NUM
ejde-1401	93	15	)	)	PUNCT
ejde-1401	93	16	we	we	PRON
ejde-1401	93	17	also	also	ADV
ejde-1401	93	18	have	have	VERB
ejde-1401	93	19	that	that	DET
ejde-1401	93	20	divg	divg	NOUN
ejde-1401	93	21	x	x	PUNCT
ejde-1401	93	22	=	=	PUNCT
ejde-1401	93	23	∆|∇u|2	∆|∇u|2	NOUN
ejde-1401	93	24	=	=	SYM
ejde-1401	93	25	2	2	NUM
ejde-1401	93	26	{	{	PUNCT
ejde-1401	93	27	|∇2u|2	|∇2u|2	PROPN
ejde-1401	93	28	−	−	NUM
ejde-1401	93	29	1	1	NUM
ejde-1401	93	30	n−	n−	NOUN
ejde-1401	93	31	1	1	NUM
ejde-1401	93	32	ric(∇u,∇u	ric(∇u,∇u	PROPN
ejde-1401	93	33	)	)	PUNCT
ejde-1401	93	34	}	}	PUNCT
ejde-1401	93	35	≥	≥	NOUN
ejde-1401	93	36	0	0	NUM
ejde-1401	93	37	.	.	PUNCT
ejde-1401	93	38	applying	apply	VERB
ejde-1401	93	39	lemma	lemma	PROPN
ejde-1401	93	40	3.1	3.1	NUM
ejde-1401	93	41	we	we	PRON
ejde-1401	93	42	conclude	conclude	VERB
ejde-1401	93	43	that	that	PRON
ejde-1401	93	44	divg(x	divg(x	NOUN
ejde-1401	93	45	)	)	PUNCT
ejde-1401	93	46	=	=	SYM
ejde-1401	94	1	0	0	X
ejde-1401	94	2	.	.	PUNCT
ejde-1401	95	1	in	in	ADP
ejde-1401	95	2	particular	particular	ADJ
ejde-1401	95	3	,	,	PUNCT
ejde-1401	95	4	we	we	PRON
ejde-1401	95	5	obtain	obtain	VERB
ejde-1401	95	6	that	that	DET
ejde-1401	95	7	|∇2u|2	|∇2u|2	PROPN
ejde-1401	95	8	=	=	SYM
ejde-1401	95	9	0	0	PUNCT
ejde-1401	95	10	and	and	CCONJ
ejde-1401	95	11	,	,	PUNCT
ejde-1401	95	12	consequently	consequently	ADV
ejde-1401	95	13	,	,	PUNCT
ejde-1401	95	14	from	from	ADP
ejde-1401	95	15	(	(	PUNCT
ejde-1401	95	16	2.2	2.2	NUM
ejde-1401	95	17	)	)	PUNCT
ejde-1401	95	18	,	,	PUNCT
ejde-1401	95	19	we	we	PRON
ejde-1401	95	20	have	have	VERB
ejde-1401	95	21	n	n	PRON
ejde-1401	95	22	m2	m2	PROPN
ejde-1401	95	23	(	(	PUNCT
ejde-1401	95	24	r−	r−	PROPN
ejde-1401	95	25	ρ)2u2	ρ)2u2	PROPN
ejde-1401	95	26	=	=	SYM
ejde-1401	95	27	0	0	X
ejde-1401	95	28	.	.	PUNCT
ejde-1401	96	1	therefore	therefore	ADV
ejde-1401	96	2	,	,	PUNCT
ejde-1401	96	3	since	since	SCONJ
ejde-1401	96	4	u	u	PROPN
ejde-1401	96	5	>	>	X
ejde-1401	96	6	0	0	NUM
ejde-1401	96	7	,	,	PUNCT
ejde-1401	96	8	we	we	PRON
ejde-1401	96	9	obtain	obtain	VERB
ejde-1401	96	10	that	that	DET
ejde-1401	96	11	r	r	NOUN
ejde-1401	96	12	=	=	SYM
ejde-1401	96	13	ρ	ρ	PROPN
ejde-1401	96	14	.	.	PUNCT
ejde-1401	96	15	□	□	PUNCT
ejde-1401	96	16	from	from	ADP
ejde-1401	96	17	kato	kato	PROPN
ejde-1401	96	18	’s	’s	PART
ejde-1401	96	19	inequality	inequality	NOUN
ejde-1401	96	20	we	we	PRON
ejde-1401	96	21	observe	observe	VERB
ejde-1401	96	22	that∣∣∇|∇u|2	that∣∣∇|∇u|2	PROPN
ejde-1401	96	23	∣∣	∣∣	PUNCT
ejde-1401	96	24	=	=	SYM
ejde-1401	96	25	2|∇u|	2|∇u|	NUM
ejde-1401	96	26	∣∣∇|∇u|	∣∣∇|∇u|	PROPN
ejde-1401	96	27	∣∣	∣∣	NUM
ejde-1401	96	28	≤	≤	NUM
ejde-1401	96	29	2|∇u|	2|∇u|	NUM
ejde-1401	96	30	|∇2u|	|∇2u|	NOUN
ejde-1401	96	31	.	.	PUNCT
ejde-1401	97	1	hence	hence	ADV
ejde-1401	97	2	,	,	PUNCT
ejde-1401	97	3	assuming	assume	VERB
ejde-1401	97	4	that	that	SCONJ
ejde-1401	97	5	|∇u|	|∇u|	ADJ
ejde-1401	97	6	∈	∈	PROPN
ejde-1401	97	7	l∞(σn	l∞(σn	NOUN
ejde-1401	97	8	)	)	PUNCT
ejde-1401	97	9	and	and	CCONJ
ejde-1401	97	10	|∇2u|	|∇2u|	NOUN
ejde-1401	97	11	∈	∈	PROPN
ejde-1401	97	12	l1(σn	l1(σn	PROPN
ejde-1401	97	13	)	)	PUNCT
ejde-1401	97	14	we	we	PRON
ejde-1401	97	15	can	can	AUX
ejde-1401	97	16	rewrite	rewrite	VERB
ejde-1401	97	17	the	the	DET
ejde-1401	97	18	theorem	theorem	ADJ
ejde-1401	97	19	3.2	3.2	NUM
ejde-1401	97	20	as	as	SCONJ
ejde-1401	97	21	follows	follow	VERB
ejde-1401	97	22	.	.	PUNCT
ejde-1401	98	1	theorem	theorem	VERB
ejde-1401	98	2	3.3	3.3	NUM
ejde-1401	98	3	.	.	PUNCT
ejde-1401	99	1	let	let	AUX
ejde-1401	99	2	(	(	PUNCT
ejde-1401	99	3	σn	σn	NOUN
ejde-1401	99	4	,	,	PUNCT
ejde-1401	99	5	g	g	NOUN
ejde-1401	99	6	,	,	PUNCT
ejde-1401	99	7	u	u	NOUN
ejde-1401	99	8	)	)	PUNCT
ejde-1401	99	9	be	be	AUX
ejde-1401	99	10	a	a	DET
ejde-1401	99	11	complete	complete	ADJ
ejde-1401	99	12	noncompact	noncompact	NOUN
ejde-1401	99	13	m	m	NOUN
ejde-1401	99	14	-	-	PUNCT
ejde-1401	99	15	quasi	quasi	ADJ
ejde-1401	99	16	yamabe	yamabe	PROPN
ejde-1401	99	17	gradient	gradient	PROPN
ejde-1401	99	18	soliton	soliton	NOUN
ejde-1401	99	19	whose	whose	DET
ejde-1401	99	20	ricci	ricci	PROPN
ejde-1401	99	21	tensor	tensor	NOUN
ejde-1401	99	22	satisfies	satisfie	NOUN
ejde-1401	99	23	ric(∇u,∇u	ric(∇u,∇u	PROPN
ejde-1401	99	24	)	)	PUNCT
ejde-1401	99	25	≤	≤	NOUN
ejde-1401	99	26	0	0	NUM
ejde-1401	99	27	,	,	PUNCT
ejde-1401	99	28	and	and	CCONJ
ejde-1401	99	29	such	such	ADJ
ejde-1401	99	30	that	that	DET
ejde-1401	99	31	|∇u|	|∇u|	ADJ
ejde-1401	99	32	∈	∈	PROPN
ejde-1401	99	33	l∞(σn	l∞(σn	NOUN
ejde-1401	99	34	)	)	PUNCT
ejde-1401	100	1	and	and	CCONJ
ejde-1401	100	2	|∇2u|	|∇2u|	NOUN
ejde-1401	100	3	∈	∈	PROPN
ejde-1401	100	4	l1(σn	l1(σn	PROPN
ejde-1401	100	5	)	)	PUNCT
ejde-1401	100	6	,	,	PUNCT
ejde-1401	100	7	then	then	ADV
ejde-1401	100	8	r	r	NOUN
ejde-1401	100	9	=	=	SYM
ejde-1401	100	10	ρ	ρ	PROPN
ejde-1401	100	11	on	on	ADP
ejde-1401	100	12	σn	σn	PROPN
ejde-1401	100	13	.	.	PUNCT
ejde-1401	101	1	at	at	ADP
ejde-1401	101	2	this	this	DET
ejde-1401	101	3	point	point	NOUN
ejde-1401	101	4	we	we	PRON
ejde-1401	101	5	recall	recall	VERB
ejde-1401	101	6	that	that	SCONJ
ejde-1401	101	7	a	a	DET
ejde-1401	101	8	smooth	smooth	ADJ
ejde-1401	101	9	function	function	NOUN
ejde-1401	101	10	u	u	PROPN
ejde-1401	101	11	∈	∈	PROPN
ejde-1401	101	12	c∞(σn	c∞(σn	NOUN
ejde-1401	101	13	)	)	PUNCT
ejde-1401	101	14	on	on	ADP
ejde-1401	101	15	a	a	DET
ejde-1401	101	16	riemannian	riemannian	ADJ
ejde-1401	101	17	manifold	manifold	ADJ
ejde-1401	101	18	σn	σn	NOUN
ejde-1401	101	19	is	be	AUX
ejde-1401	101	20	called	call	VERB
ejde-1401	101	21	a	a	DET
ejde-1401	101	22	subharmonic	subharmonic	ADJ
ejde-1401	101	23	function	function	NOUN
ejde-1401	101	24	when	when	SCONJ
ejde-1401	101	25	∆u	∆u	PROPN
ejde-1401	101	26	≥	≥	VERB
ejde-1401	101	27	0	0	NUM
ejde-1401	101	28	on	on	ADP
ejde-1401	101	29	σn	σn	PROPN
ejde-1401	101	30	.	.	PUNCT
ejde-1401	102	1	in	in	ADP
ejde-1401	102	2	this	this	DET
ejde-1401	102	3	setting	setting	NOUN
ejde-1401	102	4	,	,	PUNCT
ejde-1401	102	5	we	we	PRON
ejde-1401	102	6	present	present	VERB
ejde-1401	102	7	the	the	DET
ejde-1401	102	8	next	next	ADJ
ejde-1401	102	9	lemma	lemma	PROPN
ejde-1401	102	10	which	which	PRON
ejde-1401	102	11	is	be	AUX
ejde-1401	102	12	a	a	DET
ejde-1401	102	13	liouville	liouville	NOUN
ejde-1401	102	14	type	type	NOUN
ejde-1401	102	15	result	result	NOUN
ejde-1401	102	16	due	due	ADP
ejde-1401	102	17	to	to	ADP
ejde-1401	102	18	yau	yau	PROPN
ejde-1401	102	19	[	[	X
ejde-1401	102	20	29	29	NUM
ejde-1401	102	21	]	]	PUNCT
ejde-1401	102	22	(	(	PUNCT
ejde-1401	102	23	see	see	VERB
ejde-1401	102	24	also	also	ADV
ejde-1401	102	25	[	[	X
ejde-1401	102	26	21	21	NUM
ejde-1401	102	27	]	]	PUNCT
ejde-1401	102	28	)	)	PUNCT
ejde-1401	102	29	.	.	PUNCT
ejde-1401	103	1	lemma	lemma	PROPN
ejde-1401	103	2	3.4	3.4	NUM
ejde-1401	103	3	.	.	PUNCT
ejde-1401	104	1	let	let	VERB
ejde-1401	104	2	u	u	PRON
ejde-1401	104	3	be	be	AUX
ejde-1401	104	4	a	a	DET
ejde-1401	104	5	nonnegative	nonnegative	ADJ
ejde-1401	104	6	smooth	smooth	ADJ
ejde-1401	104	7	subharmonic	subharmonic	ADJ
ejde-1401	104	8	function	function	NOUN
ejde-1401	104	9	on	on	ADP
ejde-1401	104	10	a	a	DET
ejde-1401	104	11	complete	complete	ADJ
ejde-1401	104	12	noncompact	noncompact	NOUN
ejde-1401	104	13	riemannian	riemannian	NOUN
ejde-1401	104	14	manifold	manifold	ADJ
ejde-1401	104	15	σn	σn	NOUN
ejde-1401	104	16	.	.	PUNCT
ejde-1401	105	1	if	if	SCONJ
ejde-1401	105	2	u	u	PROPN
ejde-1401	105	3	∈	∈	PROPN
ejde-1401	105	4	lq(σn	lq(σn	NOUN
ejde-1401	105	5	)	)	PUNCT
ejde-1401	105	6	,	,	PUNCT
ejde-1401	105	7	for	for	ADP
ejde-1401	105	8	some	some	DET
ejde-1401	105	9	q	q	NOUN
ejde-1401	105	10	>	>	X
ejde-1401	105	11	1	1	NUM
ejde-1401	105	12	,	,	PUNCT
ejde-1401	105	13	then	then	ADV
ejde-1401	105	14	u	u	NOUN
ejde-1401	105	15	is	be	AUX
ejde-1401	105	16	constant	constant	ADJ
ejde-1401	105	17	.	.	PUNCT
ejde-1401	106	1	next	next	ADV
ejde-1401	106	2	,	,	PUNCT
ejde-1401	106	3	we	we	PRON
ejde-1401	106	4	will	will	AUX
ejde-1401	106	5	assume	assume	VERB
ejde-1401	106	6	that	that	SCONJ
ejde-1401	106	7	u	u	PROPN
ejde-1401	106	8	∈	∈	PROPN
ejde-1401	106	9	lq(σn	lq(σn	NOUN
ejde-1401	106	10	)	)	PUNCT
ejde-1401	106	11	,	,	PUNCT
ejde-1401	106	12	1	1	NUM
ejde-1401	106	13	<	<	X
ejde-1401	106	14	q	q	X
ejde-1401	106	15	<	<	X
ejde-1401	106	16	+	+	NOUN
ejde-1401	106	17	∞	∞	NUM
ejde-1401	106	18	and	and	CCONJ
ejde-1401	106	19	r	r	NOUN
ejde-1401	106	20	≤	≤	NUM
ejde-1401	106	21	ρ	ρ	NOUN
ejde-1401	106	22	.	.	PUNCT
ejde-1401	107	1	in	in	ADP
ejde-1401	107	2	this	this	DET
ejde-1401	107	3	way	way	NOUN
ejde-1401	107	4	,	,	PUNCT
ejde-1401	107	5	using	use	VERB
ejde-1401	107	6	lemma	lemma	PROPN
ejde-1401	107	7	3.4	3.4	NUM
ejde-1401	107	8	we	we	PRON
ejde-1401	107	9	obtain	obtain	VERB
ejde-1401	107	10	the	the	DET
ejde-1401	107	11	following	follow	VERB
ejde-1401	107	12	theorem	theorem	VERB
ejde-1401	107	13	.	.	PUNCT
ejde-1401	107	14	theorem	theorem	NOUN
ejde-1401	107	15	3.5	3.5	NUM
ejde-1401	107	16	.	.	PUNCT
ejde-1401	108	1	let	let	AUX
ejde-1401	108	2	(	(	PUNCT
ejde-1401	108	3	σn	σn	NOUN
ejde-1401	108	4	,	,	PUNCT
ejde-1401	108	5	g	g	NOUN
ejde-1401	108	6	,	,	PUNCT
ejde-1401	108	7	u	u	NOUN
ejde-1401	108	8	)	)	PUNCT
ejde-1401	108	9	be	be	AUX
ejde-1401	108	10	a	a	DET
ejde-1401	108	11	complete	complete	ADJ
ejde-1401	108	12	noncompact	noncompact	NOUN
ejde-1401	108	13	m	m	NOUN
ejde-1401	108	14	-	-	PUNCT
ejde-1401	108	15	quasi	quasi	ADJ
ejde-1401	108	16	yamabe	yamabe	PROPN
ejde-1401	108	17	gradient	gradient	NOUN
ejde-1401	108	18	soliton	soliton	NOUN
ejde-1401	109	1	such	such	ADJ
ejde-1401	109	2	that	that	SCONJ
ejde-1401	109	3	r	r	NOUN
ejde-1401	109	4	≤	≤	NUM
ejde-1401	109	5	ρ	ρ	NOUN
ejde-1401	109	6	and	and	CCONJ
ejde-1401	109	7	u	u	PROPN
ejde-1401	109	8	∈	∈	PROPN
ejde-1401	109	9	lq(σn	lq(σn	NOUN
ejde-1401	109	10	)	)	PUNCT
ejde-1401	109	11	,	,	PUNCT
ejde-1401	109	12	1	1	NUM
ejde-1401	109	13	<	<	X
ejde-1401	109	14	q	q	X
ejde-1401	109	15	<	<	X
ejde-1401	109	16	+	+	NOUN
ejde-1401	109	17	∞	∞	PROPN
ejde-1401	109	18	,	,	PUNCT
ejde-1401	109	19	then	then	ADV
ejde-1401	109	20	(	(	PUNCT
ejde-1401	109	21	σn	σn	PROPN
ejde-1401	109	22	,	,	PUNCT
ejde-1401	109	23	g	g	NOUN
ejde-1401	109	24	,	,	PUNCT
ejde-1401	109	25	u	u	NOUN
ejde-1401	109	26	)	)	PUNCT
ejde-1401	109	27	is	be	AUX
ejde-1401	109	28	trivial	trivial	ADJ
ejde-1401	109	29	and	and	CCONJ
ejde-1401	109	30	r	r	NOUN
ejde-1401	109	31	=	=	SYM
ejde-1401	109	32	ρ	ρ	PROPN
ejde-1401	109	33	on	on	ADP
ejde-1401	109	34	σn	σn	PROPN
ejde-1401	109	35	.	.	PUNCT
ejde-1401	109	36	proof	proof	NOUN
ejde-1401	109	37	.	.	PUNCT
ejde-1401	110	1	since	since	SCONJ
ejde-1401	110	2	r	r	NOUN
ejde-1401	110	3	≤	≤	NUM
ejde-1401	110	4	ρ	ρ	NOUN
ejde-1401	110	5	,	,	PUNCT
ejde-1401	110	6	from	from	ADP
ejde-1401	110	7	(	(	PUNCT
ejde-1401	110	8	2.8	2.8	NUM
ejde-1401	110	9	)	)	PUNCT
ejde-1401	110	10	we	we	PRON
ejde-1401	110	11	have	have	VERB
ejde-1401	110	12	∆u	∆u	PROPN
ejde-1401	110	13	=	=	SYM
ejde-1401	110	14	−	−	PROPN
ejde-1401	110	15	n	n	VERB
ejde-1401	110	16	m	m	PROPN
ejde-1401	110	17	(	(	PUNCT
ejde-1401	110	18	r−	r−	PROPN
ejde-1401	110	19	ρ)u	ρ)u	PROPN
ejde-1401	110	20	≥	≥	NOUN
ejde-1401	110	21	0	0	NUM
ejde-1401	110	22	.	.	PUNCT
ejde-1401	111	1	thus	thus	ADV
ejde-1401	111	2	,	,	PUNCT
ejde-1401	111	3	since	since	SCONJ
ejde-1401	111	4	we	we	PRON
ejde-1401	111	5	are	be	AUX
ejde-1401	111	6	assuming	assume	VERB
ejde-1401	111	7	u	u	PROPN
ejde-1401	111	8	∈	∈	PROPN
ejde-1401	111	9	lq(σn	lq(σn	NOUN
ejde-1401	111	10	)	)	PUNCT
ejde-1401	111	11	with	with	ADP
ejde-1401	111	12	1	1	NUM
ejde-1401	111	13	<	<	X
ejde-1401	111	14	q	q	X
ejde-1401	111	15	<	<	X
ejde-1401	111	16	+	+	PROPN
ejde-1401	111	17	∞	∞	PROPN
ejde-1401	111	18	,	,	PUNCT
ejde-1401	111	19	lemma	lemma	PROPN
ejde-1401	111	20	3.4	3.4	NUM
ejde-1401	111	21	guarantees	guarantee	NOUN
ejde-1401	111	22	that	that	SCONJ
ejde-1401	111	23	u	u	NOUN
ejde-1401	111	24	is	be	AUX
ejde-1401	111	25	constant	constant	ADJ
ejde-1401	111	26	and	and	CCONJ
ejde-1401	111	27	,	,	PUNCT
ejde-1401	111	28	hence	hence	ADV
ejde-1401	111	29	,	,	PUNCT
ejde-1401	111	30	n	n	PRON
ejde-1401	111	31	m	m	PROPN
ejde-1401	111	32	(	(	PUNCT
ejde-1401	111	33	r−	r−	PROPN
ejde-1401	111	34	ρ)u	ρ)u	PRON
ejde-1401	111	35	=	=	SYM
ejde-1401	111	36	0	0	NUM
ejde-1401	111	37	,	,	PUNCT
ejde-1401	111	38	implying	imply	VERB
ejde-1401	111	39	that	that	SCONJ
ejde-1401	111	40	r	r	NOUN
ejde-1401	111	41	=	=	SYM
ejde-1401	111	42	ρ	ρ	PROPN
ejde-1401	111	43	.	.	PUNCT
ejde-1401	112	1	□	□	PUNCT
ejde-1401	112	2	ejde-2025/62	ejde-2025/62	ADJ
ejde-1401	112	3	complete	complete	ADJ
ejde-1401	112	4	m	m	NOUN
ejde-1401	112	5	-	-	PUNCT
ejde-1401	112	6	quasi	quasi	ADJ
ejde-1401	112	7	yamabe	yamabe	PROPN
ejde-1401	112	8	gradient	gradient	PROPN
ejde-1401	112	9	solitons	soliton	NOUN
ejde-1401	112	10	5	5	NUM
ejde-1401	112	11	3.2	3.2	NUM
ejde-1401	112	12	.	.	PUNCT
ejde-1401	113	1	via	via	ADP
ejde-1401	113	2	volume	volume	NOUN
ejde-1401	113	3	growth	growth	NOUN
ejde-1401	113	4	.	.	PUNCT
ejde-1401	114	1	in	in	ADP
ejde-1401	114	2	this	this	DET
ejde-1401	114	3	subsection	subsection	NOUN
ejde-1401	114	4	we	we	PRON
ejde-1401	114	5	deal	deal	VERB
ejde-1401	114	6	with	with	ADP
ejde-1401	114	7	the	the	DET
ejde-1401	114	8	notion	notion	NOUN
ejde-1401	114	9	of	of	ADP
ejde-1401	114	10	volume	volume	NOUN
ejde-1401	114	11	growth	growth	NOUN
ejde-1401	114	12	.	.	PUNCT
ejde-1401	115	1	let	let	VERB
ejde-1401	115	2	us	we	PRON
ejde-1401	115	3	consider	consider	VERB
ejde-1401	115	4	a	a	DET
ejde-1401	115	5	(	(	PUNCT
ejde-1401	115	6	connected	connected	ADJ
ejde-1401	115	7	oriented	oriented	ADJ
ejde-1401	115	8	)	)	PUNCT
ejde-1401	115	9	complete	complete	ADJ
ejde-1401	115	10	riemannian	riemannian	ADJ
ejde-1401	115	11	manifold	manifold	NOUN
ejde-1401	115	12	(	(	PUNCT
ejde-1401	115	13	σn	σn	PROPN
ejde-1401	115	14	,	,	PUNCT
ejde-1401	115	15	g	g	NOUN
ejde-1401	115	16	)	)	PUNCT
ejde-1401	115	17	and	and	CCONJ
ejde-1401	115	18	denote	denote	VERB
ejde-1401	115	19	by	by	ADP
ejde-1401	115	20	b(p	b(p	PROPN
ejde-1401	115	21	,	,	PUNCT
ejde-1401	115	22	t	t	PROPN
ejde-1401	115	23	)	)	PUNCT
ejde-1401	115	24	a	a	DET
ejde-1401	115	25	geodesic	geodesic	NOUN
ejde-1401	115	26	ball	ball	NOUN
ejde-1401	115	27	centered	center	VERB
ejde-1401	115	28	at	at	ADP
ejde-1401	115	29	p	p	NOUN
ejde-1401	115	30	and	and	CCONJ
ejde-1401	115	31	with	with	ADP
ejde-1401	115	32	radius	radius	NOUN
ejde-1401	115	33	t.	t.	NOUN
ejde-1401	115	34	given	give	VERB
ejde-1401	115	35	a	a	DET
ejde-1401	115	36	continuous	continuous	ADJ
ejde-1401	115	37	function	function	NOUN
ejde-1401	115	38	σ	σ	NOUN
ejde-1401	115	39	:	:	PUNCT
ejde-1401	115	40	(	(	PUNCT
ejde-1401	115	41	0,+∞	0,+∞	NUM
ejde-1401	115	42	)	)	PUNCT
ejde-1401	115	43	→	→	SYM
ejde-1401	115	44	(	(	PUNCT
ejde-1401	115	45	0,+∞	0,+∞	NUM
ejde-1401	115	46	)	)	PUNCT
ejde-1401	116	1	we	we	PRON
ejde-1401	116	2	say	say	VERB
ejde-1401	116	3	that	that	SCONJ
ejde-1401	116	4	σn	σn	PROPN
ejde-1401	116	5	has	have	VERB
ejde-1401	116	6	volume	volume	NOUN
ejde-1401	116	7	growth	growth	NOUN
ejde-1401	116	8	like	like	ADP
ejde-1401	116	9	σ(t	σ(t	NOUN
ejde-1401	116	10	)	)	PUNCT
ejde-1401	116	11	if	if	SCONJ
ejde-1401	116	12	there	there	PRON
ejde-1401	116	13	exists	exist	VERB
ejde-1401	116	14	p	p	PROPN
ejde-1401	116	15	∈	∈	PROPN
ejde-1401	116	16	σn	σn	NOUN
ejde-1401	116	17	such	such	ADJ
ejde-1401	116	18	that	that	DET
ejde-1401	116	19	vol(b(p	vol(b(p	NOUN
ejde-1401	116	20	,	,	PUNCT
ejde-1401	116	21	t	t	PROPN
ejde-1401	116	22	)	)	PUNCT
ejde-1401	116	23	)	)	PUNCT
ejde-1401	117	1	=	=	SYM
ejde-1401	117	2	o(σ(t	o(σ(t	PROPN
ejde-1401	117	3	)	)	PUNCT
ejde-1401	117	4	)	)	PUNCT
ejde-1401	117	5	as	as	ADP
ejde-1401	117	6	t	t	PROPN
ejde-1401	117	7	→	→	SYM
ejde-1401	117	8	∞	∞	PROPN
ejde-1401	117	9	,	,	PUNCT
ejde-1401	117	10	where	where	SCONJ
ejde-1401	117	11	vol	vol	NOUN
ejde-1401	117	12	stands	stand	VERB
ejde-1401	117	13	the	the	DET
ejde-1401	117	14	volume	volume	NOUN
ejde-1401	117	15	,	,	PUNCT
ejde-1401	117	16	that	that	ADV
ejde-1401	117	17	is	is	ADV
ejde-1401	117	18	,	,	PUNCT
ejde-1401	117	19	vol(b(p	vol(b(p	PROPN
ejde-1401	117	20	,	,	PUNCT
ejde-1401	117	21	t	t	PROPN
ejde-1401	117	22	)	)	PUNCT
ejde-1401	117	23	)	)	PUNCT
ejde-1401	118	1	=	=	SYM
ejde-1401	119	1	∫	∫	PROPN
ejde-1401	119	2	b(p	b(p	PROPN
ejde-1401	119	3	,	,	PUNCT
ejde-1401	119	4	t	t	PROPN
ejde-1401	119	5	)	)	PUNCT
ejde-1401	119	6	dς	dς	PROPN
ejde-1401	119	7	.	.	PUNCT
ejde-1401	120	1	with	with	ADP
ejde-1401	120	2	the	the	DET
ejde-1401	120	3	above	above	ADJ
ejde-1401	120	4	concept	concept	NOUN
ejde-1401	120	5	in	in	ADP
ejde-1401	120	6	mind	mind	NOUN
ejde-1401	120	7	,	,	PUNCT
ejde-1401	120	8	we	we	PRON
ejde-1401	120	9	can	can	AUX
ejde-1401	120	10	present	present	VERB
ejde-1401	120	11	the	the	DET
ejde-1401	120	12	following	follow	VERB
ejde-1401	120	13	lemma	lemma	PROPN
ejde-1401	120	14	which	which	PRON
ejde-1401	120	15	corresponds	correspond	VERB
ejde-1401	120	16	to	to	ADP
ejde-1401	120	17	a	a	DET
ejde-1401	120	18	particular	particular	ADJ
ejde-1401	120	19	case	case	NOUN
ejde-1401	120	20	of	of	ADP
ejde-1401	120	21	a	a	DET
ejde-1401	120	22	more	more	ADV
ejde-1401	120	23	general	general	ADJ
ejde-1401	120	24	maximum	maximum	ADJ
ejde-1401	120	25	principle	principle	NOUN
ejde-1401	120	26	due	due	ADP
ejde-1401	120	27	to	to	ADP
ejde-1401	120	28	aĺıas	aĺıa	NOUN
ejde-1401	120	29	,	,	PUNCT
ejde-1401	120	30	caminha	caminha	NOUN
ejde-1401	120	31	and	and	CCONJ
ejde-1401	120	32	nascimento	nascimento	PROPN
ejde-1401	120	33	(	(	PUNCT
ejde-1401	120	34	see	see	VERB
ejde-1401	120	35	[	[	X
ejde-1401	120	36	2	2	NUM
ejde-1401	120	37	,	,	PUNCT
ejde-1401	120	38	theorem	theorem	VERB
ejde-1401	120	39	2.1	2.1	NUM
ejde-1401	120	40	]	]	PUNCT
ejde-1401	120	41	)	)	PUNCT
ejde-1401	120	42	.	.	PUNCT
ejde-1401	121	1	lemma	lemma	PROPN
ejde-1401	121	2	3.6	3.6	NUM
ejde-1401	121	3	.	.	PUNCT
ejde-1401	122	1	let	let	AUX
ejde-1401	122	2	(	(	PUNCT
ejde-1401	122	3	σn	σn	NOUN
ejde-1401	122	4	,	,	PUNCT
ejde-1401	122	5	g	g	NOUN
ejde-1401	122	6	)	)	PUNCT
ejde-1401	122	7	be	be	AUX
ejde-1401	122	8	a	a	DET
ejde-1401	122	9	complete	complete	ADJ
ejde-1401	122	10	noncompact	noncompact	NOUN
ejde-1401	122	11	riemannian	riemannian	NOUN
ejde-1401	122	12	manifold	manifold	NOUN
ejde-1401	122	13	and	and	CCONJ
ejde-1401	122	14	let	let	VERB
ejde-1401	122	15	x	x	PROPN
ejde-1401	122	16	∈	∈	PROPN
ejde-1401	122	17	x(σn	x(σn	PROPN
ejde-1401	122	18	)	)	PUNCT
ejde-1401	122	19	be	be	VERB
ejde-1401	122	20	a	a	DET
ejde-1401	122	21	bounded	bounded	ADJ
ejde-1401	122	22	smooth	smooth	ADJ
ejde-1401	122	23	vector	vector	NOUN
ejde-1401	122	24	field	field	NOUN
ejde-1401	122	25	on	on	ADP
ejde-1401	122	26	σn	σn	NOUN
ejde-1401	122	27	,	,	PUNCT
ejde-1401	122	28	with	with	ADP
ejde-1401	122	29	|x|	|x|	PROPN
ejde-1401	122	30	≤	≤	NUM
ejde-1401	122	31	c	c	NOUN
ejde-1401	122	32	for	for	SCONJ
ejde-1401	122	33	some	some	DET
ejde-1401	122	34	positive	positive	ADJ
ejde-1401	122	35	constant	constant	ADJ
ejde-1401	122	36	c	c	PROPN
ejde-1401	122	37	∈	∈	PROPN
ejde-1401	122	38	r.	r.	PROPN
ejde-1401	122	39	let	let	VERB
ejde-1401	122	40	v	v	ADP
ejde-1401	122	41	∈	∈	PROPN
ejde-1401	122	42	c∞(σ	c∞(σ	NOUN
ejde-1401	122	43	)	)	PUNCT
ejde-1401	122	44	be	be	VERB
ejde-1401	122	45	a	a	DET
ejde-1401	122	46	smooth	smooth	ADJ
ejde-1401	122	47	function	function	NOUN
ejde-1401	122	48	such	such	ADJ
ejde-1401	122	49	that	that	SCONJ
ejde-1401	122	50	g(∇v	g(∇v	NOUN
ejde-1401	122	51	,	,	PUNCT
ejde-1401	122	52	x	x	X
ejde-1401	122	53	)	)	PUNCT
ejde-1401	122	54	≥	≥	NOUN
ejde-1401	122	55	0	0	NUM
ejde-1401	122	56	and	and	CCONJ
ejde-1401	122	57	divg	divg	NOUN
ejde-1401	122	58	x	x	SYM
ejde-1401	122	59	≥	≥	NUM
ejde-1401	122	60	av	av	PROPN
ejde-1401	122	61	on	on	ADP
ejde-1401	122	62	σn	σn	PROPN
ejde-1401	122	63	,	,	PUNCT
ejde-1401	122	64	for	for	ADP
ejde-1401	122	65	some	some	DET
ejde-1401	122	66	positive	positive	ADJ
ejde-1401	122	67	constant	constant	NOUN
ejde-1401	122	68	a	a	DET
ejde-1401	122	69	∈	∈	PROPN
ejde-1401	122	70	r.	r.	NOUN
ejde-1401	122	71	(	(	PUNCT
ejde-1401	122	72	i	i	NOUN
ejde-1401	122	73	)	)	PUNCT
ejde-1401	122	74	if	if	SCONJ
ejde-1401	122	75	(	(	PUNCT
ejde-1401	122	76	σn	σn	NOUN
ejde-1401	122	77	,	,	PUNCT
ejde-1401	122	78	g	g	NOUN
ejde-1401	122	79	)	)	PUNCT
ejde-1401	122	80	has	have	VERB
ejde-1401	122	81	polynomial	polynomial	ADJ
ejde-1401	122	82	volume	volume	NOUN
ejde-1401	122	83	growth	growth	NOUN
ejde-1401	122	84	,	,	PUNCT
ejde-1401	122	85	then	then	ADV
ejde-1401	122	86	v	v	X
ejde-1401	122	87	≤	≤	NOUN
ejde-1401	122	88	0	0	NUM
ejde-1401	122	89	on	on	ADP
ejde-1401	122	90	σn	σn	PROPN
ejde-1401	122	91	.	.	PUNCT
ejde-1401	122	92	(	(	PUNCT
ejde-1401	122	93	ii	ii	NOUN
ejde-1401	122	94	)	)	PUNCT
ejde-1401	122	95	if	if	SCONJ
ejde-1401	122	96	(	(	PUNCT
ejde-1401	122	97	σn	σn	NOUN
ejde-1401	122	98	,	,	PUNCT
ejde-1401	122	99	g	g	NOUN
ejde-1401	122	100	)	)	PUNCT
ejde-1401	122	101	has	have	VERB
ejde-1401	122	102	exponential	exponential	ADJ
ejde-1401	122	103	volume	volume	NOUN
ejde-1401	122	104	growth	growth	NOUN
ejde-1401	122	105	,	,	PUNCT
ejde-1401	122	106	say	say	VERB
ejde-1401	122	107	like	like	ADP
ejde-1401	122	108	eβt	eβt	NOUN
ejde-1401	122	109	,	,	PUNCT
ejde-1401	122	110	then	then	ADV
ejde-1401	122	111	v	v	X
ejde-1401	122	112	≤	≤	NUM
ejde-1401	122	113	cβ	cβ	NOUN
ejde-1401	122	114	a	a	PRON
ejde-1401	122	115	on	on	ADP
ejde-1401	122	116	σn	σn	NOUN
ejde-1401	122	117	.	.	PUNCT
ejde-1401	123	1	using	use	VERB
ejde-1401	123	2	this	this	DET
ejde-1401	123	3	previous	previous	ADJ
ejde-1401	123	4	lemma	lemma	PROPN
ejde-1401	123	5	,	,	PUNCT
ejde-1401	123	6	we	we	PRON
ejde-1401	123	7	obtain	obtain	VERB
ejde-1401	123	8	the	the	DET
ejde-1401	123	9	following	follow	VERB
ejde-1401	123	10	nonexistence	nonexistence	NOUN
ejde-1401	123	11	result	result	NOUN
ejde-1401	123	12	concerning	concern	VERB
ejde-1401	123	13	complete	complete	ADJ
ejde-1401	123	14	noncompact	noncompact	NOUN
ejde-1401	123	15	m	m	PROPN
ejde-1401	123	16	-	-	PUNCT
ejde-1401	123	17	quasi	quasi	ADJ
ejde-1401	123	18	yamabe	yamabe	PROPN
ejde-1401	123	19	gradient	gradient	PROPN
ejde-1401	123	20	soliton	soliton	NOUN
ejde-1401	123	21	.	.	PUNCT
ejde-1401	124	1	theorem	theorem	VERB
ejde-1401	124	2	3.7	3.7	NUM
ejde-1401	124	3	.	.	PUNCT
ejde-1401	125	1	there	there	PRON
ejde-1401	125	2	is	be	VERB
ejde-1401	125	3	no	no	DET
ejde-1401	125	4	a	a	DET
ejde-1401	125	5	complete	complete	ADJ
ejde-1401	125	6	noncompact	noncompact	NOUN
ejde-1401	125	7	m	m	NOUN
ejde-1401	125	8	-	-	PUNCT
ejde-1401	125	9	quasi	quasi	ADJ
ejde-1401	125	10	yamabe	yamabe	PROPN
ejde-1401	125	11	gradient	gradient	PROPN
ejde-1401	125	12	soliton	soliton	NOUN
ejde-1401	125	13	(	(	PUNCT
ejde-1401	125	14	σn	σn	PROPN
ejde-1401	125	15	,	,	PUNCT
ejde-1401	125	16	g	g	NOUN
ejde-1401	125	17	,	,	PUNCT
ejde-1401	125	18	u	u	NOUN
ejde-1401	125	19	)	)	PUNCT
ejde-1401	125	20	with	with	ADP
ejde-1401	125	21	polynomial	polynomial	ADJ
ejde-1401	125	22	volume	volume	NOUN
ejde-1401	125	23	growth	growth	NOUN
ejde-1401	125	24	such	such	DET
ejde-1401	125	25	that	that	DET
ejde-1401	125	26	|∇u|	|∇u|	ADJ
ejde-1401	125	27	∈	∈	PROPN
ejde-1401	125	28	l∞(σn	l∞(σn	NOUN
ejde-1401	125	29	)	)	PUNCT
ejde-1401	125	30	and	and	CCONJ
ejde-1401	125	31	r	r	NOUN
ejde-1401	125	32	≤	≤	NUM
ejde-1401	125	33	ρ−α	ρ−α	NOUN
ejde-1401	125	34	,	,	PUNCT
ejde-1401	125	35	for	for	ADP
ejde-1401	125	36	some	some	DET
ejde-1401	125	37	positive	positive	ADJ
ejde-1401	125	38	constant	constant	ADJ
ejde-1401	125	39	α	α	PROPN
ejde-1401	125	40	∈	∈	PROPN
ejde-1401	125	41	r.	r.	NOUN
ejde-1401	125	42	proof	proof	NOUN
ejde-1401	125	43	.	.	PUNCT
ejde-1401	126	1	suppose	suppose	VERB
ejde-1401	126	2	by	by	ADP
ejde-1401	126	3	contradiction	contradiction	NOUN
ejde-1401	126	4	the	the	DET
ejde-1401	126	5	existence	existence	NOUN
ejde-1401	126	6	of	of	ADP
ejde-1401	126	7	such	such	DET
ejde-1401	126	8	a	a	DET
ejde-1401	126	9	complete	complete	ADJ
ejde-1401	126	10	m	m	NOUN
ejde-1401	126	11	-	-	PUNCT
ejde-1401	126	12	quasi	quasi	ADJ
ejde-1401	126	13	yamabe	yamabe	PROPN
ejde-1401	126	14	gradient	gradient	PROPN
ejde-1401	126	15	soliton	soliton	NOUN
ejde-1401	126	16	(	(	PUNCT
ejde-1401	126	17	σn	σn	PROPN
ejde-1401	126	18	,	,	PUNCT
ejde-1401	126	19	g	g	NOUN
ejde-1401	126	20	,	,	PUNCT
ejde-1401	126	21	u	u	NOUN
ejde-1401	126	22	)	)	PUNCT
ejde-1401	126	23	.	.	PUNCT
ejde-1401	127	1	so	so	ADV
ejde-1401	127	2	,	,	PUNCT
ejde-1401	127	3	let	let	VERB
ejde-1401	127	4	us	we	PRON
ejde-1401	127	5	take	take	VERB
ejde-1401	127	6	the	the	DET
ejde-1401	127	7	smooth	smooth	ADJ
ejde-1401	127	8	vector	vector	NOUN
ejde-1401	127	9	field	field	NOUN
ejde-1401	127	10	x	x	PUNCT
ejde-1401	127	11	=	=	PUNCT
ejde-1401	127	12	∇u	∇u	PROPN
ejde-1401	127	13	∈	∈	PROPN
ejde-1401	127	14	x(σn	x(σn	PROPN
ejde-1401	127	15	)	)	PUNCT
ejde-1401	127	16	.	.	PUNCT
ejde-1401	128	1	we	we	PRON
ejde-1401	128	2	point	point	VERB
ejde-1401	128	3	out	out	ADP
ejde-1401	128	4	that	that	SCONJ
ejde-1401	128	5	u	u	PROPN
ejde-1401	128	6	is	be	AUX
ejde-1401	128	7	a	a	DET
ejde-1401	128	8	smooth	smooth	ADJ
ejde-1401	128	9	function	function	NOUN
ejde-1401	128	10	such	such	ADJ
ejde-1401	128	11	that	that	SCONJ
ejde-1401	128	12	g(∇u	g(∇u	NUM
ejde-1401	128	13	,	,	PUNCT
ejde-1401	128	14	x	x	X
ejde-1401	128	15	)	)	PUNCT
ejde-1401	128	16	=	=	SYM
ejde-1401	128	17	g(∇u,∇u	g(∇u,∇u	NOUN
ejde-1401	128	18	)	)	PUNCT
ejde-1401	128	19	≥	≥	NOUN
ejde-1401	128	20	0	0	NUM
ejde-1401	128	21	.	.	PUNCT
ejde-1401	129	1	since	since	SCONJ
ejde-1401	129	2	we	we	PRON
ejde-1401	129	3	are	be	AUX
ejde-1401	129	4	supposing	suppose	VERB
ejde-1401	129	5	that	that	SCONJ
ejde-1401	129	6	r	r	NOUN
ejde-1401	129	7	≤	≤	NUM
ejde-1401	129	8	ρ−	ρ−	PROPN
ejde-1401	129	9	α	α	NOUN
ejde-1401	129	10	,	,	PUNCT
ejde-1401	129	11	we	we	PRON
ejde-1401	129	12	obtain	obtain	VERB
ejde-1401	129	13	divg	divg	NOUN
ejde-1401	129	14	x	x	X
ejde-1401	130	1	=	=	PUNCT
ejde-1401	130	2	∆u	∆u	PROPN
ejde-1401	130	3	=	=	SYM
ejde-1401	130	4	−	−	PROPN
ejde-1401	130	5	n	n	VERB
ejde-1401	130	6	m	m	PROPN
ejde-1401	130	7	(	(	PUNCT
ejde-1401	130	8	r−	r−	PROPN
ejde-1401	130	9	ρ)u	ρ)u	PROPN
ejde-1401	130	10	≥	≥	NOUN
ejde-1401	130	11	nα	nα	ADP
ejde-1401	130	12	m	m	NOUN
ejde-1401	130	13	u.	u.	NOUN
ejde-1401	130	14	hence	hence	ADV
ejde-1401	130	15	,	,	PUNCT
ejde-1401	130	16	since	since	SCONJ
ejde-1401	130	17	σn	σn	NOUN
ejde-1401	130	18	is	be	AUX
ejde-1401	130	19	complete	complete	ADJ
ejde-1401	130	20	noncompact	noncompact	NOUN
ejde-1401	130	21	we	we	PRON
ejde-1401	130	22	can	can	AUX
ejde-1401	130	23	apply	apply	VERB
ejde-1401	130	24	item	item	NOUN
ejde-1401	130	25	(	(	PUNCT
ejde-1401	130	26	i	i	NOUN
ejde-1401	130	27	)	)	PUNCT
ejde-1401	130	28	of	of	ADP
ejde-1401	130	29	lemma	lemma	PROPN
ejde-1401	130	30	3.6	3.6	NUM
ejde-1401	130	31	to	to	PART
ejde-1401	130	32	conclude	conclude	VERB
ejde-1401	130	33	that	that	SCONJ
ejde-1401	130	34	u	u	PROPN
ejde-1401	130	35	≤	≤	ADV
ejde-1401	130	36	0	0	NUM
ejde-1401	130	37	,	,	PUNCT
ejde-1401	130	38	leading	lead	VERB
ejde-1401	130	39	us	we	PRON
ejde-1401	130	40	to	to	ADP
ejde-1401	130	41	an	an	DET
ejde-1401	130	42	absurd	absurd	ADJ
ejde-1401	130	43	.	.	PUNCT
ejde-1401	131	1	□	□	PUNCT
ejde-1401	131	2	next	next	ADV
ejde-1401	131	3	,	,	PUNCT
ejde-1401	131	4	we	we	PRON
ejde-1401	131	5	will	will	AUX
ejde-1401	131	6	use	use	VERB
ejde-1401	131	7	bochner	bochn	ADJ
ejde-1401	131	8	type	type	NOUN
ejde-1401	131	9	formula	formula	NOUN
ejde-1401	131	10	(	(	PUNCT
ejde-1401	131	11	2.10	2.10	NUM
ejde-1401	131	12	)	)	PUNCT
ejde-1401	131	13	to	to	PART
ejde-1401	131	14	obtain	obtain	VERB
ejde-1401	131	15	the	the	DET
ejde-1401	131	16	following	follow	VERB
ejde-1401	131	17	characterization	characterization	NOUN
ejde-1401	131	18	result	result	NOUN
ejde-1401	131	19	.	.	PUNCT
ejde-1401	132	1	theorem	theorem	VERB
ejde-1401	132	2	3.8	3.8	NUM
ejde-1401	132	3	.	.	PUNCT
ejde-1401	133	1	let	let	AUX
ejde-1401	133	2	(	(	PUNCT
ejde-1401	133	3	σn	σn	NOUN
ejde-1401	133	4	,	,	PUNCT
ejde-1401	133	5	g	g	NOUN
ejde-1401	133	6	,	,	PUNCT
ejde-1401	133	7	u	u	NOUN
ejde-1401	133	8	)	)	PUNCT
ejde-1401	133	9	be	be	AUX
ejde-1401	133	10	a	a	DET
ejde-1401	133	11	complete	complete	ADJ
ejde-1401	133	12	noncompact	noncompact	NOUN
ejde-1401	133	13	m	m	NOUN
ejde-1401	133	14	-	-	PUNCT
ejde-1401	133	15	quasi	quasi	ADJ
ejde-1401	133	16	yamabe	yamabe	PROPN
ejde-1401	133	17	gradient	gradient	PROPN
ejde-1401	133	18	soliton	soliton	NOUN
ejde-1401	133	19	whose	whose	DET
ejde-1401	133	20	ricci	ricci	PROPN
ejde-1401	133	21	tensor	tensor	NOUN
ejde-1401	133	22	satisfies	satisfie	NOUN
ejde-1401	133	23	ric(∇u,∇u	ric(∇u,∇u	PROPN
ejde-1401	133	24	)	)	PUNCT
ejde-1401	133	25	≤	≤	PROPN
ejde-1401	133	26	−α|∇u|2	−α|∇u|2	NUM
ejde-1401	133	27	,	,	PUNCT
ejde-1401	133	28	for	for	ADP
ejde-1401	133	29	some	some	DET
ejde-1401	133	30	positive	positive	ADJ
ejde-1401	133	31	constant	constant	ADJ
ejde-1401	133	32	α	α	PROPN
ejde-1401	133	33	∈	∈	PROPN
ejde-1401	133	34	r.	r.	PROPN
ejde-1401	133	35	if	if	SCONJ
ejde-1401	133	36	(	(	PUNCT
ejde-1401	133	37	σn	σn	NOUN
ejde-1401	133	38	,	,	PUNCT
ejde-1401	133	39	g	g	NOUN
ejde-1401	133	40	)	)	PUNCT
ejde-1401	133	41	has	have	VERB
ejde-1401	133	42	polynomial	polynomial	ADJ
ejde-1401	133	43	volume	volume	NOUN
ejde-1401	133	44	growth	growth	NOUN
ejde-1401	133	45	and	and	CCONJ
ejde-1401	133	46	|∇u|	|∇u|	NOUN
ejde-1401	133	47	,	,	PUNCT
ejde-1401	133	48	|∇2u|	|∇2u|	NOUN
ejde-1401	133	49	∈	∈	PROPN
ejde-1401	133	50	l∞(σn	l∞(σn	NOUN
ejde-1401	133	51	)	)	PUNCT
ejde-1401	133	52	,	,	PUNCT
ejde-1401	133	53	then	then	ADV
ejde-1401	133	54	(	(	PUNCT
ejde-1401	133	55	σn	σn	PROPN
ejde-1401	133	56	,	,	PUNCT
ejde-1401	133	57	g	g	NOUN
ejde-1401	133	58	,	,	PUNCT
ejde-1401	133	59	u	u	NOUN
ejde-1401	133	60	)	)	PUNCT
ejde-1401	133	61	is	be	AUX
ejde-1401	133	62	trivial	trivial	ADJ
ejde-1401	133	63	and	and	CCONJ
ejde-1401	133	64	r	r	NOUN
ejde-1401	133	65	=	=	SYM
ejde-1401	133	66	ρ	ρ	PROPN
ejde-1401	133	67	on	on	ADP
ejde-1401	133	68	σn	σn	PROPN
ejde-1401	133	69	.	.	PUNCT
ejde-1401	134	1	proof	proof	NOUN
ejde-1401	134	2	.	.	PUNCT
ejde-1401	135	1	taking	take	VERB
ejde-1401	135	2	the	the	DET
ejde-1401	135	3	smooth	smooth	ADJ
ejde-1401	135	4	vector	vector	NOUN
ejde-1401	135	5	field	field	NOUN
ejde-1401	135	6	x	x	PUNCT
ejde-1401	135	7	=	=	PUNCT
ejde-1401	135	8	∇|∇u|2	∇|∇u|2	PROPN
ejde-1401	135	9	∈	∈	PROPN
ejde-1401	135	10	x(σn	x(σn	PROPN
ejde-1401	135	11	)	)	PUNCT
ejde-1401	135	12	and	and	CCONJ
ejde-1401	135	13	the	the	DET
ejde-1401	135	14	smooth	smooth	ADJ
ejde-1401	135	15	function	function	NOUN
ejde-1401	135	16	v	v	ADP
ejde-1401	135	17	=	=	PUNCT
ejde-1401	135	18	|∇u|2	|∇u|2	NOUN
ejde-1401	135	19	∈	∈	PROPN
ejde-1401	135	20	c∞(σn	c∞(σn	NOUN
ejde-1401	135	21	)	)	PUNCT
ejde-1401	135	22	,	,	PUNCT
ejde-1401	135	23	by	by	ADP
ejde-1401	135	24	using	use	VERB
ejde-1401	135	25	again	again	ADV
ejde-1401	135	26	kato	kato	PROPN
ejde-1401	135	27	’s	’s	PART
ejde-1401	135	28	inequality	inequality	NOUN
ejde-1401	135	29	we	we	PRON
ejde-1401	135	30	have	have	VERB
ejde-1401	135	31	that	that	DET
ejde-1401	135	32	|x|	|x|	PROPN
ejde-1401	135	33	=	=	SYM
ejde-1401	135	34	|∇|∇u|2|	|∇|∇u|2|	PROPN
ejde-1401	135	35	=	=	SYM
ejde-1401	135	36	2|∇u||∇|∇u||	2|∇u||∇|∇u||	NUM
ejde-1401	135	37	≤	≤	ADJ
ejde-1401	135	38	2|∇u||∇2u|	2|∇u||∇2u|	PROPN
ejde-1401	135	39	.	.	PUNCT
ejde-1401	136	1	so	so	ADV
ejde-1401	136	2	,	,	PUNCT
ejde-1401	136	3	since	since	SCONJ
ejde-1401	136	4	|∇u|	|∇u|	NUM
ejde-1401	136	5	,	,	PUNCT
ejde-1401	136	6	|∇2u|	|∇2u|	NOUN
ejde-1401	136	7	∈	∈	PROPN
ejde-1401	136	8	l∞(σn	l∞(σn	NOUN
ejde-1401	136	9	)	)	PUNCT
ejde-1401	136	10	,	,	PUNCT
ejde-1401	136	11	we	we	PRON
ejde-1401	136	12	see	see	VERB
ejde-1401	136	13	that	that	SCONJ
ejde-1401	136	14	x	x	PRON
ejde-1401	136	15	is	be	AUX
ejde-1401	136	16	a	a	DET
ejde-1401	136	17	bounded	bounded	ADJ
ejde-1401	136	18	smooth	smooth	ADJ
ejde-1401	136	19	vector	vector	NOUN
ejde-1401	136	20	field	field	NOUN
ejde-1401	136	21	.	.	PUNCT
ejde-1401	137	1	moreover	moreover	ADV
ejde-1401	137	2	,	,	PUNCT
ejde-1401	137	3	we	we	PRON
ejde-1401	137	4	also	also	ADV
ejde-1401	137	5	have	have	VERB
ejde-1401	137	6	that	that	PRON
ejde-1401	137	7	g(x,∇v	g(x,∇v	VERB
ejde-1401	137	8	)	)	PUNCT
ejde-1401	137	9	=	=	SYM
ejde-1401	137	10	g(∇|∇u|2,∇|∇u|2	g(∇|∇u|2,∇|∇u|2	PROPN
ejde-1401	137	11	)	)	PUNCT
ejde-1401	137	12	≥	≥	NOUN
ejde-1401	137	13	0	0	NUM
ejde-1401	137	14	.	.	PUNCT
ejde-1401	138	1	furthermore	furthermore	ADV
ejde-1401	138	2	,	,	PUNCT
ejde-1401	138	3	since	since	SCONJ
ejde-1401	138	4	ric(∇u,∇u	ric(∇u,∇u	PROPN
ejde-1401	138	5	)	)	PUNCT
ejde-1401	138	6	≤	≤	PROPN
ejde-1401	138	7	−α|∇u|2	−α|∇u|2	NOUN
ejde-1401	138	8	,	,	PUNCT
ejde-1401	138	9	from	from	ADP
ejde-1401	138	10	(	(	PUNCT
ejde-1401	138	11	2.10	2.10	NUM
ejde-1401	138	12	)	)	PUNCT
ejde-1401	138	13	we	we	PRON
ejde-1401	138	14	infer	infer	VERB
ejde-1401	138	15	that	that	SCONJ
ejde-1401	138	16	divg	divg	NOUN
ejde-1401	138	17	x	x	PUNCT
ejde-1401	139	1	=	=	PUNCT
ejde-1401	139	2	∆|∇u|2	∆|∇u|2	NOUN
ejde-1401	139	3	≥	≥	NUM
ejde-1401	139	4	2α	2α	NOUN
ejde-1401	139	5	n−	n−	NOUN
ejde-1401	139	6	1	1	NUM
ejde-1401	139	7	|∇u|2	|∇u|2	NOUN
ejde-1401	139	8	.	.	PUNCT
ejde-1401	139	9	6	6	NUM
ejde-1401	139	10	g.	g.	PROPN
ejde-1401	139	11	molica	molica	PROPN
ejde-1401	139	12	bisci	bisci	PROPN
ejde-1401	139	13	,	,	PUNCT
ejde-1401	139	14	h.	h.	PROPN
ejde-1401	139	15	f.	f.	PROPN
ejde-1401	139	16	de	de	PROPN
ejde-1401	139	17	lima	lima	PROPN
ejde-1401	139	18	,	,	PUNCT
ejde-1401	139	19	a.	a.	PROPN
ejde-1401	139	20	v.	v.	PROPN
ejde-1401	139	21	f.	f.	PROPN
ejde-1401	139	22	leite	leite	PROPN
ejde-1401	139	23	,	,	PUNCT
ejde-1401	139	24	m.	m.	NOUN
ejde-1401	139	25	a.	a.	PROPN
ejde-1401	139	26	l.	l.	PROPN
ejde-1401	139	27	velásquez	velásquez	PROPN
ejde-1401	139	28	ejde-2025/62	ejde-2025/62	PROPN
ejde-1401	139	29	hence	hence	ADV
ejde-1401	139	30	,	,	PUNCT
ejde-1401	139	31	since	since	SCONJ
ejde-1401	139	32	σn	σn	NOUN
ejde-1401	139	33	is	be	AUX
ejde-1401	139	34	complete	complete	ADJ
ejde-1401	139	35	noncompact	noncompact	NOUN
ejde-1401	139	36	,	,	PUNCT
ejde-1401	139	37	we	we	PRON
ejde-1401	139	38	can	can	AUX
ejde-1401	139	39	apply	apply	VERB
ejde-1401	139	40	item	item	NOUN
ejde-1401	139	41	(	(	PUNCT
ejde-1401	139	42	i	i	NOUN
ejde-1401	139	43	)	)	PUNCT
ejde-1401	139	44	of	of	ADP
ejde-1401	139	45	lemma	lemma	PROPN
ejde-1401	139	46	3.6	3.6	NUM
ejde-1401	139	47	to	to	PART
ejde-1401	139	48	conclude	conclude	VERB
ejde-1401	139	49	that	that	PRON
ejde-1401	139	50	|∇u|2	|∇u|2	NOUN
ejde-1401	139	51	=	=	SYM
ejde-1401	139	52	0	0	PUNCT
ejde-1401	139	53	and	and	CCONJ
ejde-1401	139	54	,	,	PUNCT
ejde-1401	139	55	consequently	consequently	ADV
ejde-1401	139	56	,	,	PUNCT
ejde-1401	139	57	u	u	PRON
ejde-1401	139	58	must	must	AUX
ejde-1401	139	59	be	be	AUX
ejde-1401	139	60	a	a	DET
ejde-1401	139	61	positive	positive	ADJ
ejde-1401	139	62	constant	constant	NOUN
ejde-1401	139	63	.	.	PUNCT
ejde-1401	140	1	thus	thus	ADV
ejde-1401	140	2	,	,	PUNCT
ejde-1401	140	3	we	we	PRON
ejde-1401	140	4	also	also	ADV
ejde-1401	140	5	have	have	VERB
ejde-1401	140	6	0	0	NUM
ejde-1401	140	7	=	=	SYM
ejde-1401	140	8	1	1	NUM
ejde-1401	140	9	2	2	NUM
ejde-1401	140	10	∆|∇u|2	∆|∇u|2	NOUN
ejde-1401	140	11	≥	≥	NOUN
ejde-1401	140	12	|∇2u|2	|∇2u|2	PROPN
ejde-1401	140	13	=	=	SYM
ejde-1401	140	14	n	n	NUM
ejde-1401	140	15	m2	m2	PROPN
ejde-1401	140	16	(	(	PUNCT
ejde-1401	140	17	r−	r−	PROPN
ejde-1401	140	18	ρ)2u2	ρ)2u2	PROPN
ejde-1401	140	19	≥	≥	NOUN
ejde-1401	140	20	0	0	NUM
ejde-1401	140	21	,	,	PUNCT
ejde-1401	140	22	implying	imply	VERB
ejde-1401	140	23	that	that	SCONJ
ejde-1401	140	24	r	r	NOUN
ejde-1401	140	25	=	=	SYM
ejde-1401	140	26	ρ	ρ	PROPN
ejde-1401	140	27	.	.	PUNCT
ejde-1401	141	1	□	□	PUNCT
ejde-1401	141	2	proceeding	proceeding	NOUN
ejde-1401	141	3	,	,	PUNCT
ejde-1401	141	4	we	we	PRON
ejde-1401	141	5	will	will	AUX
ejde-1401	141	6	deal	deal	VERB
ejde-1401	141	7	with	with	ADP
ejde-1401	141	8	complete	complete	ADJ
ejde-1401	141	9	noncompact	noncompact	NOUN
ejde-1401	141	10	m	m	PROPN
ejde-1401	141	11	-	-	PUNCT
ejde-1401	141	12	quasi	quasi	ADJ
ejde-1401	141	13	yamabe	yamabe	PROPN
ejde-1401	141	14	gradient	gradient	PROPN
ejde-1401	141	15	solitons	soliton	NOUN
ejde-1401	141	16	having	have	VERB
ejde-1401	141	17	exponential	exponential	ADJ
ejde-1401	141	18	volume	volume	NOUN
ejde-1401	141	19	growth	growth	NOUN
ejde-1401	141	20	.	.	PUNCT
ejde-1401	142	1	theorem	theorem	VERB
ejde-1401	142	2	3.9	3.9	NUM
ejde-1401	142	3	.	.	PUNCT
ejde-1401	143	1	let	let	AUX
ejde-1401	143	2	(	(	PUNCT
ejde-1401	143	3	σn	σn	NOUN
ejde-1401	143	4	,	,	PUNCT
ejde-1401	143	5	g	g	NOUN
ejde-1401	143	6	,	,	PUNCT
ejde-1401	143	7	u	u	NOUN
ejde-1401	143	8	)	)	PUNCT
ejde-1401	143	9	be	be	AUX
ejde-1401	143	10	a	a	DET
ejde-1401	143	11	complete	complete	ADJ
ejde-1401	143	12	noncompact	noncompact	NOUN
ejde-1401	143	13	m	m	NOUN
ejde-1401	143	14	-	-	PUNCT
ejde-1401	143	15	quasi	quasi	ADJ
ejde-1401	143	16	yamabe	yamabe	ADJ
ejde-1401	143	17	gradient	gradient	PROPN
ejde-1401	143	18	soliton	soliton	NOUN
ejde-1401	143	19	with	with	ADP
ejde-1401	143	20	exponential	exponential	ADJ
ejde-1401	143	21	volume	volume	NOUN
ejde-1401	143	22	growth	growth	NOUN
ejde-1401	143	23	,	,	PUNCT
ejde-1401	143	24	say	say	VERB
ejde-1401	143	25	like	like	ADP
ejde-1401	143	26	eβt	eβt	NOUN
ejde-1401	143	27	.	.	PUNCT
ejde-1401	144	1	if	if	SCONJ
ejde-1401	144	2	|∇u|	|∇u|	PROPN
ejde-1401	144	3	∈	∈	PROPN
ejde-1401	144	4	l∞(σn	l∞(σn	NOUN
ejde-1401	144	5	)	)	PUNCT
ejde-1401	144	6	and	and	CCONJ
ejde-1401	144	7	r	r	NOUN
ejde-1401	144	8	≤	≤	NUM
ejde-1401	144	9	ρ	ρ	NOUN
ejde-1401	144	10	−	−	PROPN
ejde-1401	144	11	α	α	NOUN
ejde-1401	144	12	,	,	PUNCT
ejde-1401	144	13	for	for	ADP
ejde-1401	144	14	some	some	DET
ejde-1401	144	15	positive	positive	ADJ
ejde-1401	144	16	constant	constant	ADJ
ejde-1401	144	17	α	α	PRON
ejde-1401	144	18	∈	∈	PROPN
ejde-1401	144	19	r	r	NOUN
ejde-1401	144	20	,	,	PUNCT
ejde-1401	144	21	then	then	ADV
ejde-1401	144	22	|u|∞	|u|∞	PROPN
ejde-1401	144	23	≤	≤	PROPN
ejde-1401	144	24	mβ	mβ	AUX
ejde-1401	144	25	nα	nα	PRON
ejde-1401	144	26	|∇u|∞.	|∇u|∞.	ADJ
ejde-1401	144	27	proof	proof	NOUN
ejde-1401	144	28	.	.	PUNCT
ejde-1401	145	1	taking	take	VERB
ejde-1401	145	2	the	the	DET
ejde-1401	145	3	smooth	smooth	ADJ
ejde-1401	145	4	vector	vector	NOUN
ejde-1401	145	5	field	field	NOUN
ejde-1401	145	6	x	x	PUNCT
ejde-1401	145	7	=	=	PUNCT
ejde-1401	145	8	∇u	∇u	PROPN
ejde-1401	145	9	∈	∈	PROPN
ejde-1401	145	10	x(σn	x(σn	PROPN
ejde-1401	145	11	)	)	PUNCT
ejde-1401	145	12	and	and	CCONJ
ejde-1401	145	13	following	follow	VERB
ejde-1401	145	14	the	the	DET
ejde-1401	145	15	same	same	ADJ
ejde-1401	145	16	steps	step	NOUN
ejde-1401	145	17	of	of	ADP
ejde-1401	145	18	the	the	DET
ejde-1401	145	19	proof	proof	NOUN
ejde-1401	145	20	of	of	ADP
ejde-1401	145	21	theorem	theorem	ADJ
ejde-1401	145	22	3.7	3.7	NUM
ejde-1401	145	23	we	we	PRON
ejde-1401	145	24	obtain	obtain	VERB
ejde-1401	145	25	that	that	SCONJ
ejde-1401	145	26	x	x	PRON
ejde-1401	145	27	is	be	AUX
ejde-1401	145	28	a	a	DET
ejde-1401	145	29	bounded	bounded	ADJ
ejde-1401	145	30	smooth	smooth	ADJ
ejde-1401	145	31	vector	vector	NOUN
ejde-1401	145	32	field	field	NOUN
ejde-1401	145	33	,	,	PUNCT
ejde-1401	145	34	g(∇u	g(∇u	NUM
ejde-1401	145	35	,	,	PUNCT
ejde-1401	145	36	x	x	X
ejde-1401	145	37	)	)	PUNCT
ejde-1401	145	38	≥	≥	NOUN
ejde-1401	145	39	0	0	NUM
ejde-1401	145	40	and	and	CCONJ
ejde-1401	145	41	divg	divg	NOUN
ejde-1401	145	42	x	x	PUNCT
ejde-1401	145	43	≥	≥	NOUN
ejde-1401	146	1	nα	nα	PROPN
ejde-1401	146	2	m	m	NOUN
ejde-1401	146	3	u.	u.	NOUN
ejde-1401	146	4	hence	hence	ADV
ejde-1401	146	5	,	,	PUNCT
ejde-1401	146	6	applying	apply	VERB
ejde-1401	146	7	item	item	NOUN
ejde-1401	146	8	(	(	PUNCT
ejde-1401	146	9	ii	ii	NOUN
ejde-1401	146	10	)	)	PUNCT
ejde-1401	146	11	of	of	ADP
ejde-1401	146	12	lemma	lemma	PROPN
ejde-1401	146	13	3.6	3.6	NUM
ejde-1401	146	14	we	we	PRON
ejde-1401	146	15	obtain	obtain	VERB
ejde-1401	146	16	|u|	|u|	ADJ
ejde-1401	146	17	≤	≤	NUM
ejde-1401	146	18	mβ	mβ	VERB
ejde-1401	146	19	nα	nα	ADP
ejde-1401	146	20	|∇u|∞.	|∇u|∞.	VERB
ejde-1401	146	21	therefore	therefore	ADV
ejde-1401	146	22	,	,	PUNCT
ejde-1401	146	23	we	we	PRON
ejde-1401	146	24	conclude	conclude	VERB
ejde-1401	146	25	that	that	SCONJ
ejde-1401	146	26	|u|∞	|u|∞	ADJ
ejde-1401	146	27	≤	≤	PUNCT
ejde-1401	146	28	mβ	mβ	AUX
ejde-1401	146	29	nα	nα	ADP
ejde-1401	146	30	|∇u|∞.	|∇u|∞.	VERB
ejde-1401	146	31	□	□	PUNCT
ejde-1401	146	32	to	to	PART
ejde-1401	146	33	finish	finish	VERB
ejde-1401	146	34	this	this	DET
ejde-1401	146	35	subsection	subsection	NOUN
ejde-1401	146	36	we	we	PRON
ejde-1401	146	37	will	will	AUX
ejde-1401	146	38	present	present	VERB
ejde-1401	146	39	one	one	NUM
ejde-1401	146	40	more	more	ADJ
ejde-1401	146	41	result	result	NOUN
ejde-1401	146	42	concerning	concern	VERB
ejde-1401	146	43	exponential	exponential	ADJ
ejde-1401	146	44	volume	volume	NOUN
ejde-1401	146	45	growth	growth	NOUN
ejde-1401	146	46	of	of	ADP
ejde-1401	146	47	a	a	DET
ejde-1401	146	48	complete	complete	ADJ
ejde-1401	146	49	noncompact	noncompact	NOUN
ejde-1401	146	50	m	m	NOUN
ejde-1401	146	51	-	-	PUNCT
ejde-1401	146	52	quasi	quasi	ADJ
ejde-1401	146	53	yamabe	yamabe	PROPN
ejde-1401	146	54	gradient	gradient	PROPN
ejde-1401	146	55	soliton	soliton	NOUN
ejde-1401	146	56	.	.	PUNCT
ejde-1401	147	1	theorem	theorem	VERB
ejde-1401	147	2	3.10	3.10	NUM
ejde-1401	147	3	.	.	PUNCT
ejde-1401	148	1	let	let	AUX
ejde-1401	148	2	(	(	PUNCT
ejde-1401	148	3	σn	σn	NOUN
ejde-1401	148	4	,	,	PUNCT
ejde-1401	148	5	g	g	NOUN
ejde-1401	148	6	,	,	PUNCT
ejde-1401	148	7	u	u	NOUN
ejde-1401	148	8	)	)	PUNCT
ejde-1401	148	9	be	be	AUX
ejde-1401	148	10	a	a	DET
ejde-1401	148	11	complete	complete	ADJ
ejde-1401	148	12	noncompact	noncompact	NOUN
ejde-1401	148	13	m	m	NOUN
ejde-1401	148	14	-	-	PUNCT
ejde-1401	148	15	quasi	quasi	ADJ
ejde-1401	148	16	yamabe	yamabe	ADJ
ejde-1401	148	17	gradient	gradient	PROPN
ejde-1401	148	18	soliton	soliton	NOUN
ejde-1401	148	19	with	with	ADP
ejde-1401	148	20	exponential	exponential	ADJ
ejde-1401	148	21	volume	volume	NOUN
ejde-1401	148	22	growth	growth	NOUN
ejde-1401	148	23	,	,	PUNCT
ejde-1401	148	24	say	say	VERB
ejde-1401	148	25	like	like	ADP
ejde-1401	148	26	eβt	eβt	NOUN
ejde-1401	148	27	.	.	PUNCT
ejde-1401	149	1	if	if	SCONJ
ejde-1401	149	2	|∇u|	|∇u|	NOUN
ejde-1401	149	3	,	,	PUNCT
ejde-1401	149	4	|∇2u|	|∇2u|	NOUN
ejde-1401	149	5	∈	∈	PROPN
ejde-1401	149	6	l∞(σn	l∞(σn	NOUN
ejde-1401	149	7	)	)	PUNCT
ejde-1401	149	8	and	and	CCONJ
ejde-1401	149	9	ric(∇u,∇u	ric(∇u,∇u	PROPN
ejde-1401	149	10	)	)	PUNCT
ejde-1401	149	11	≤	≤	NOUN
ejde-1401	149	12	−α|∇u|2	−α|∇u|2	NUM
ejde-1401	149	13	,	,	PUNCT
ejde-1401	149	14	for	for	ADP
ejde-1401	149	15	some	some	DET
ejde-1401	149	16	positive	positive	ADJ
ejde-1401	149	17	constant	constant	ADJ
ejde-1401	149	18	α	α	PRON
ejde-1401	149	19	∈	∈	PROPN
ejde-1401	149	20	r	r	NOUN
ejde-1401	149	21	,	,	PUNCT
ejde-1401	149	22	then	then	ADV
ejde-1401	149	23	|∇u|∞	|∇u|∞	VERB
ejde-1401	149	24	≤	≤	NOUN
ejde-1401	149	25	(	(	PUNCT
ejde-1401	149	26	n−	n−	NOUN
ejde-1401	149	27	1)β	1)β	NUM
ejde-1401	149	28	2α	2α	NOUN
ejde-1401	149	29	|∇2u|∞.	|∇2u|∞.	ADJ
ejde-1401	149	30	proof	proof	NOUN
ejde-1401	149	31	.	.	PUNCT
ejde-1401	150	1	taking	take	VERB
ejde-1401	150	2	the	the	DET
ejde-1401	150	3	smooth	smooth	ADJ
ejde-1401	150	4	vector	vector	NOUN
ejde-1401	150	5	field	field	NOUN
ejde-1401	150	6	x	x	PUNCT
ejde-1401	150	7	=	=	PUNCT
ejde-1401	150	8	∇|∇u|2	∇|∇u|2	PROPN
ejde-1401	150	9	∈	∈	PROPN
ejde-1401	150	10	x(σn	x(σn	PROPN
ejde-1401	150	11	)	)	PUNCT
ejde-1401	150	12	and	and	CCONJ
ejde-1401	150	13	following	follow	VERB
ejde-1401	150	14	the	the	DET
ejde-1401	150	15	same	same	ADJ
ejde-1401	150	16	steps	step	NOUN
ejde-1401	150	17	of	of	ADP
ejde-1401	150	18	the	the	DET
ejde-1401	150	19	proof	proof	NOUN
ejde-1401	150	20	of	of	ADP
ejde-1401	150	21	theorem	theorem	ADJ
ejde-1401	150	22	3.8	3.8	NUM
ejde-1401	150	23	we	we	PRON
ejde-1401	150	24	obtain	obtain	VERB
ejde-1401	150	25	that	that	SCONJ
ejde-1401	150	26	x	x	PRON
ejde-1401	150	27	is	be	AUX
ejde-1401	150	28	a	a	DET
ejde-1401	150	29	bounded	bounded	ADJ
ejde-1401	150	30	smooth	smooth	ADJ
ejde-1401	150	31	vector	vector	NOUN
ejde-1401	150	32	field	field	NOUN
ejde-1401	150	33	,	,	PUNCT
ejde-1401	150	34	g(∇|∇u|2	g(∇|∇u|2	PROPN
ejde-1401	150	35	,	,	PUNCT
ejde-1401	150	36	x	x	NOUN
ejde-1401	150	37	)	)	PUNCT
ejde-1401	150	38	≥	≥	NOUN
ejde-1401	150	39	0	0	NUM
ejde-1401	150	40	and	and	CCONJ
ejde-1401	150	41	divg	divg	NOUN
ejde-1401	150	42	x	x	PUNCT
ejde-1401	150	43	≥	≥	NUM
ejde-1401	150	44	2α	2α	PROPN
ejde-1401	150	45	n−1	n−1	PROPN
ejde-1401	150	46	|∇u|2	|∇u|2	NOUN
ejde-1401	150	47	.	.	PUNCT
ejde-1401	151	1	so	so	ADV
ejde-1401	151	2	,	,	PUNCT
ejde-1401	151	3	applying	apply	VERB
ejde-1401	151	4	item	item	NOUN
ejde-1401	151	5	(	(	PUNCT
ejde-1401	151	6	ii	ii	NOUN
ejde-1401	151	7	)	)	PUNCT
ejde-1401	151	8	of	of	ADP
ejde-1401	151	9	lemma	lemma	PROPN
ejde-1401	151	10	3.6	3.6	NUM
ejde-1401	151	11	we	we	PRON
ejde-1401	151	12	obtain	obtain	VERB
ejde-1401	151	13	|∇u|2	|∇u|2	NOUN
ejde-1401	151	14	≤	≤	NOUN
ejde-1401	151	15	(	(	PUNCT
ejde-1401	151	16	n−	n−	NOUN
ejde-1401	151	17	1)β	1)β	NUM
ejde-1401	151	18	2α	2α	NOUN
ejde-1401	151	19	|∇u|∞|∇2u|∞.	|∇u|∞|∇2u|∞.	NOUN
ejde-1401	151	20	thus	thus	ADV
ejde-1401	151	21	,	,	PUNCT
ejde-1401	151	22	we	we	PRON
ejde-1401	151	23	conclude	conclude	VERB
ejde-1401	151	24	that	that	SCONJ
ejde-1401	151	25	|∇u|∞	|∇u|∞	ADJ
ejde-1401	151	26	≤	≤	NOUN
ejde-1401	151	27	(	(	PUNCT
ejde-1401	151	28	n−	n−	NOUN
ejde-1401	151	29	1)β	1)β	NOUN
ejde-1401	151	30	2α	2α	VERB
ejde-1401	151	31	|∇2u|∞.	|∇2u|∞.	PROPN
ejde-1401	151	32	□	□	PUNCT
ejde-1401	151	33	3.3	3.3	NUM
ejde-1401	151	34	.	.	PUNCT
ejde-1401	152	1	via	via	ADP
ejde-1401	152	2	stochastic	stochastic	ADJ
ejde-1401	152	3	completeness	completeness	NOUN
ejde-1401	152	4	.	.	PUNCT
ejde-1401	153	1	we	we	PRON
ejde-1401	153	2	recall	recall	VERB
ejde-1401	153	3	that	that	SCONJ
ejde-1401	153	4	a	a	DET
ejde-1401	153	5	riemannian	riemannian	ADJ
ejde-1401	153	6	manifold	manifold	NOUN
ejde-1401	153	7	(	(	PUNCT
ejde-1401	153	8	σn	σn	PROPN
ejde-1401	153	9	,	,	PUNCT
ejde-1401	153	10	g	g	NOUN
ejde-1401	153	11	)	)	PUNCT
ejde-1401	153	12	is	be	AUX
ejde-1401	153	13	said	say	VERB
ejde-1401	153	14	to	to	PART
ejde-1401	153	15	be	be	AUX
ejde-1401	153	16	stochastically	stochastically	ADV
ejde-1401	153	17	complete	complete	ADJ
ejde-1401	153	18	if	if	SCONJ
ejde-1401	153	19	,	,	PUNCT
ejde-1401	153	20	for	for	ADP
ejde-1401	153	21	some	some	PRON
ejde-1401	153	22	(	(	PUNCT
ejde-1401	153	23	and	and	CCONJ
ejde-1401	153	24	,	,	PUNCT
ejde-1401	153	25	hence	hence	ADV
ejde-1401	153	26	,	,	PUNCT
ejde-1401	153	27	for	for	ADP
ejde-1401	153	28	any	any	PRON
ejde-1401	153	29	)	)	PUNCT
ejde-1401	153	30	(	(	PUNCT
ejde-1401	153	31	x	x	X
ejde-1401	153	32	,	,	PUNCT
ejde-1401	153	33	τ	τ	X
ejde-1401	153	34	)	)	PUNCT
ejde-1401	153	35	∈	∈	PROPN
ejde-1401	153	36	σn	σn	X
ejde-1401	153	37	×	×	NOUN
ejde-1401	153	38	(	(	PUNCT
ejde-1401	153	39	0,+∞	0,+∞	NUM
ejde-1401	153	40	)	)	PUNCT
ejde-1401	153	41	,	,	PUNCT
ejde-1401	153	42	the	the	DET
ejde-1401	153	43	heat	heat	NOUN
ejde-1401	153	44	kernel	kernel	PROPN
ejde-1401	153	45	p(x	p(x	PROPN
ejde-1401	153	46	,	,	PUNCT
ejde-1401	153	47	y	y	PROPN
ejde-1401	153	48	,	,	PUNCT
ejde-1401	153	49	τ	τ	PROPN
ejde-1401	153	50	)	)	PUNCT
ejde-1401	153	51	of	of	ADP
ejde-1401	153	52	the	the	DET
ejde-1401	153	53	laplace	laplace	NOUN
ejde-1401	153	54	-	-	PUNCT
ejde-1401	153	55	beltrami	beltrami	ADJ
ejde-1401	153	56	operator	operator	NOUN
ejde-1401	153	57	∆	∆	PROPN
ejde-1401	153	58	satisfies	satisfy	VERB
ejde-1401	153	59	the	the	DET
ejde-1401	153	60	conservation	conservation	NOUN
ejde-1401	153	61	property∫	property∫	NOUN
ejde-1401	153	62	σ	σ	X
ejde-1401	153	63	p(x	p(x	PROPN
ejde-1401	153	64	,	,	PUNCT
ejde-1401	153	65	y	y	PROPN
ejde-1401	153	66	,	,	PUNCT
ejde-1401	153	67	τ)dµ(y	τ)dµ(y	NUM
ejde-1401	153	68	)	)	PUNCT
ejde-1401	153	69	=	=	SYM
ejde-1401	154	1	1	1	X
ejde-1401	154	2	.	.	PUNCT
ejde-1401	154	3	(	(	PUNCT
ejde-1401	154	4	3.1	3.1	NUM
ejde-1401	154	5	)	)	PUNCT
ejde-1401	154	6	from	from	ADP
ejde-1401	154	7	the	the	DET
ejde-1401	154	8	probabilistic	probabilistic	ADJ
ejde-1401	154	9	viewpoint	viewpoint	NOUN
ejde-1401	154	10	,	,	PUNCT
ejde-1401	154	11	stochastically	stochastically	ADV
ejde-1401	154	12	completeness	completeness	NOUN
ejde-1401	154	13	is	be	AUX
ejde-1401	154	14	the	the	DET
ejde-1401	154	15	property	property	NOUN
ejde-1401	154	16	of	of	ADP
ejde-1401	154	17	a	a	DET
ejde-1401	154	18	stochastic	stochastic	ADJ
ejde-1401	154	19	process	process	NOUN
ejde-1401	154	20	to	to	PART
ejde-1401	154	21	have	have	VERB
ejde-1401	154	22	infinite	infinite	ADJ
ejde-1401	154	23	life	life	NOUN
ejde-1401	154	24	time	time	NOUN
ejde-1401	154	25	.	.	PUNCT
ejde-1401	155	1	furthermore	furthermore	ADV
ejde-1401	155	2	,	,	PUNCT
ejde-1401	155	3	for	for	ADP
ejde-1401	155	4	the	the	DET
ejde-1401	155	5	brownian	brownian	ADJ
ejde-1401	155	6	motion	motion	NOUN
ejde-1401	155	7	on	on	ADP
ejde-1401	155	8	a	a	DET
ejde-1401	155	9	manifold	manifold	NOUN
ejde-1401	155	10	,	,	PUNCT
ejde-1401	155	11	the	the	DET
ejde-1401	155	12	conservation	conservation	NOUN
ejde-1401	155	13	property	property	NOUN
ejde-1401	155	14	(	(	PUNCT
ejde-1401	155	15	3.1	3.1	NUM
ejde-1401	155	16	)	)	PUNCT
ejde-1401	155	17	means	mean	VERB
ejde-1401	155	18	that	that	SCONJ
ejde-1401	155	19	the	the	DET
ejde-1401	155	20	total	total	ADJ
ejde-1401	155	21	probability	probability	NOUN
ejde-1401	155	22	of	of	ADP
ejde-1401	155	23	the	the	DET
ejde-1401	155	24	particle	particle	NOUN
ejde-1401	155	25	to	to	PART
ejde-1401	155	26	be	be	AUX
ejde-1401	155	27	found	find	VERB
ejde-1401	155	28	in	in	ADP
ejde-1401	155	29	the	the	DET
ejde-1401	155	30	state	state	NOUN
ejde-1401	155	31	space	space	NOUN
ejde-1401	155	32	is	be	AUX
ejde-1401	155	33	constantly	constantly	ADV
ejde-1401	155	34	equal	equal	ADJ
ejde-1401	155	35	to	to	ADP
ejde-1401	155	36	one	one	NUM
ejde-1401	155	37	(	(	PUNCT
ejde-1401	155	38	cf	cf	NOUN
ejde-1401	155	39	.	.	PUNCT
ejde-1401	156	1	[	[	X
ejde-1401	156	2	8	8	NUM
ejde-1401	156	3	,	,	PUNCT
ejde-1401	156	4	10	10	NUM
ejde-1401	156	5	,	,	PUNCT
ejde-1401	156	6	11	11	NUM
ejde-1401	156	7	,	,	PUNCT
ejde-1401	156	8	24	24	NUM
ejde-1401	156	9	]	]	PUNCT
ejde-1401	156	10	)	)	PUNCT
ejde-1401	156	11	.	.	PUNCT
ejde-1401	157	1	on	on	ADP
ejde-1401	157	2	the	the	DET
ejde-1401	157	3	other	other	ADJ
ejde-1401	157	4	hand	hand	NOUN
ejde-1401	157	5	,	,	PUNCT
ejde-1401	157	6	following	follow	VERB
ejde-1401	157	7	the	the	DET
ejde-1401	157	8	terminology	terminology	NOUN
ejde-1401	157	9	introduced	introduce	VERB
ejde-1401	157	10	by	by	ADP
ejde-1401	157	11	pigola	pigola	PROPN
ejde-1401	157	12	,	,	PUNCT
ejde-1401	157	13	rigoli	rigoli	NOUN
ejde-1401	157	14	and	and	CCONJ
ejde-1401	157	15	setti	setti	NOUN
ejde-1401	157	16	in	in	ADP
ejde-1401	157	17	[	[	X
ejde-1401	157	18	20	20	NUM
ejde-1401	157	19	]	]	PUNCT
ejde-1401	157	20	,	,	PUNCT
ejde-1401	157	21	the	the	DET
ejde-1401	157	22	omori	omori	PROPN
ejde-1401	157	23	-	-	PUNCT
ejde-1401	157	24	yau	yau	PROPN
ejde-1401	157	25	’s	’s	PART
ejde-1401	157	26	maximum	maximum	ADJ
ejde-1401	157	27	principle	principle	NOUN
ejde-1401	157	28	is	be	AUX
ejde-1401	157	29	said	say	VERB
ejde-1401	157	30	to	to	PART
ejde-1401	157	31	hold	hold	VERB
ejde-1401	157	32	on	on	ADP
ejde-1401	157	33	a	a	DET
ejde-1401	157	34	(	(	PUNCT
ejde-1401	157	35	not	not	PART
ejde-1401	157	36	necessarily	necessarily	ADV
ejde-1401	157	37	complete	complete	ADJ
ejde-1401	157	38	)	)	PUNCT
ejde-1401	157	39	n	n	CCONJ
ejde-1401	157	40	-	-	PUNCT
ejde-1401	157	41	dimensional	dimensional	ADJ
ejde-1401	157	42	ejde-2025/62	ejde-2025/62	ADJ
ejde-1401	157	43	complete	complete	ADJ
ejde-1401	157	44	m	m	NOUN
ejde-1401	157	45	-	-	PUNCT
ejde-1401	157	46	quasi	quasi	ADJ
ejde-1401	157	47	yamabe	yamabe	PROPN
ejde-1401	157	48	gradient	gradient	PROPN
ejde-1401	157	49	solitons	soliton	NOUN
ejde-1401	157	50	7	7	NUM
ejde-1401	157	51	riemannian	riemannian	NOUN
ejde-1401	157	52	manifold	manifold	NOUN
ejde-1401	157	53	(	(	PUNCT
ejde-1401	157	54	σn	σn	PROPN
ejde-1401	157	55	,	,	PUNCT
ejde-1401	157	56	g	g	NOUN
ejde-1401	157	57	)	)	PUNCT
ejde-1401	157	58	if	if	SCONJ
ejde-1401	157	59	,	,	PUNCT
ejde-1401	157	60	for	for	ADP
ejde-1401	157	61	any	any	DET
ejde-1401	157	62	smooth	smooth	ADJ
ejde-1401	157	63	function	function	NOUN
ejde-1401	157	64	u	u	PROPN
ejde-1401	157	65	∈	∈	PROPN
ejde-1401	157	66	c2(σn	c2(σn	PROPN
ejde-1401	157	67	)	)	PUNCT
ejde-1401	157	68	with	with	ADP
ejde-1401	157	69	supς	supς	NOUN
ejde-1401	157	70	u	u	X
ejde-1401	157	71	<	<	X
ejde-1401	157	72	+	+	NOUN
ejde-1401	157	73	∞	∞	PROPN
ejde-1401	157	74	,	,	PUNCT
ejde-1401	157	75	there	there	PRON
ejde-1401	157	76	exists	exist	VERB
ejde-1401	157	77	a	a	DET
ejde-1401	157	78	sequence	sequence	NOUN
ejde-1401	157	79	of	of	ADP
ejde-1401	157	80	points	point	NOUN
ejde-1401	157	81	(	(	PUNCT
ejde-1401	157	82	pk	pk	NOUN
ejde-1401	157	83	)	)	PUNCT
ejde-1401	157	84	⊂	⊂	PROPN
ejde-1401	158	1	σn	σn	PROPN
ejde-1401	158	2	satisfying	satisfy	VERB
ejde-1401	158	3	lim	lim	PROPN
ejde-1401	158	4	k	k	PROPN
ejde-1401	158	5	u(pk	u(pk	PROPN
ejde-1401	158	6	)	)	PUNCT
ejde-1401	158	7	=	=	SYM
ejde-1401	158	8	sup	sup	NOUN
ejde-1401	158	9	σ	σ	NUM
ejde-1401	158	10	u	u	PROPN
ejde-1401	158	11	,	,	PUNCT
ejde-1401	158	12	lim	lim	PROPN
ejde-1401	158	13	k	k	PROPN
ejde-1401	158	14	|∇u(pk)|	|∇u(pk)|	PROPN
ejde-1401	159	1	=	=	PUNCT
ejde-1401	159	2	0	0	PROPN
ejde-1401	159	3	and	and	CCONJ
ejde-1401	159	4	lim	lim	PROPN
ejde-1401	159	5	sup	sup	PROPN
ejde-1401	159	6	k	k	PROPN
ejde-1401	159	7	∆u(pk	∆u(pk	ADV
ejde-1401	159	8	)	)	PUNCT
ejde-1401	159	9	≤	≤	NOUN
ejde-1401	159	10	0	0	NUM
ejde-1401	159	11	.	.	PUNCT
ejde-1401	160	1	in	in	ADP
ejde-1401	160	2	this	this	DET
ejde-1401	160	3	point	point	NOUN
ejde-1401	160	4	of	of	ADP
ejde-1401	160	5	view	view	NOUN
ejde-1401	160	6	,	,	PUNCT
ejde-1401	160	7	the	the	DET
ejde-1401	160	8	classical	classical	ADJ
ejde-1401	160	9	result	result	NOUN
ejde-1401	160	10	given	give	VERB
ejde-1401	160	11	by	by	ADP
ejde-1401	160	12	omori	omori	PROPN
ejde-1401	160	13	and	and	CCONJ
ejde-1401	160	14	yau	yau	PROPN
ejde-1401	160	15	in	in	ADP
ejde-1401	160	16	[	[	X
ejde-1401	160	17	18	18	NUM
ejde-1401	160	18	,	,	PUNCT
ejde-1401	160	19	29	29	NUM
ejde-1401	160	20	]	]	PUNCT
ejde-1401	160	21	states	state	VERB
ejde-1401	160	22	that	that	SCONJ
ejde-1401	160	23	omori	omori	NOUN
ejde-1401	160	24	-	-	PUNCT
ejde-1401	160	25	yau	yau	PROPN
ejde-1401	160	26	’s	’s	PART
ejde-1401	160	27	maximum	maximum	ADJ
ejde-1401	160	28	principle	principle	NOUN
ejde-1401	160	29	holds	hold	VERB
ejde-1401	160	30	on	on	ADP
ejde-1401	160	31	every	every	DET
ejde-1401	160	32	complete	complete	ADJ
ejde-1401	160	33	riemannian	riemannian	NOUN
ejde-1401	160	34	manifold	manifold	NOUN
ejde-1401	160	35	with	with	ADP
ejde-1401	160	36	ricci	ricci	PROPN
ejde-1401	160	37	curvature	curvature	PROPN
ejde-1401	160	38	bounded	bound	VERB
ejde-1401	160	39	from	from	ADP
ejde-1401	160	40	below	below	ADV
ejde-1401	160	41	.	.	PUNCT
ejde-1401	161	1	but	but	CCONJ
ejde-1401	161	2	,	,	PUNCT
ejde-1401	161	3	as	as	SCONJ
ejde-1401	161	4	it	it	PRON
ejde-1401	161	5	was	be	AUX
ejde-1401	161	6	also	also	ADV
ejde-1401	161	7	observed	observe	VERB
ejde-1401	161	8	by	by	ADP
ejde-1401	161	9	pigola	pigola	PROPN
ejde-1401	161	10	,	,	PUNCT
ejde-1401	161	11	rigoli	rigoli	NOUN
ejde-1401	161	12	and	and	CCONJ
ejde-1401	161	13	setti	setti	NOUN
ejde-1401	161	14	in	in	ADP
ejde-1401	161	15	[	[	X
ejde-1401	161	16	20	20	NUM
ejde-1401	161	17	]	]	PUNCT
ejde-1401	161	18	,	,	PUNCT
ejde-1401	161	19	the	the	DET
ejde-1401	161	20	validity	validity	NOUN
ejde-1401	161	21	of	of	ADP
ejde-1401	161	22	omori	omori	PROPN
ejde-1401	161	23	-	-	PUNCT
ejde-1401	161	24	yau	yau	PROPN
ejde-1401	161	25	’s	’s	PART
ejde-1401	161	26	maximum	maximum	ADJ
ejde-1401	161	27	principle	principle	NOUN
ejde-1401	161	28	on	on	ADP
ejde-1401	161	29	σn	σn	NOUN
ejde-1401	161	30	does	do	AUX
ejde-1401	161	31	not	not	PART
ejde-1401	161	32	depend	depend	VERB
ejde-1401	161	33	on	on	ADP
ejde-1401	161	34	curvature	curvature	NOUN
ejde-1401	161	35	bounds	bound	NOUN
ejde-1401	161	36	as	as	SCONJ
ejde-1401	161	37	would	would	AUX
ejde-1401	161	38	be	be	AUX
ejde-1401	161	39	expected	expect	VERB
ejde-1401	161	40	.	.	PUNCT
ejde-1401	162	1	for	for	ADP
ejde-1401	162	2	instance	instance	NOUN
ejde-1401	162	3	,	,	PUNCT
ejde-1401	162	4	the	the	DET
ejde-1401	162	5	omori	omori	PROPN
ejde-1401	162	6	-	-	PUNCT
ejde-1401	162	7	yau	yau	PROPN
ejde-1401	162	8	’s	’s	PART
ejde-1401	162	9	maximum	maximum	ADJ
ejde-1401	162	10	principle	principle	NOUN
ejde-1401	162	11	holds	hold	VERB
ejde-1401	162	12	on	on	ADP
ejde-1401	162	13	every	every	DET
ejde-1401	162	14	riemannian	riemannian	ADJ
ejde-1401	162	15	manifolds	manifold	NOUN
ejde-1401	162	16	which	which	PRON
ejde-1401	162	17	is	be	AUX
ejde-1401	162	18	properly	properly	ADV
ejde-1401	162	19	immersed	immerse	VERB
ejde-1401	162	20	into	into	ADP
ejde-1401	162	21	a	a	DET
ejde-1401	162	22	riemannian	riemannian	ADJ
ejde-1401	162	23	space	space	NOUN
ejde-1401	162	24	form	form	NOUN
ejde-1401	162	25	with	with	ADP
ejde-1401	162	26	controlled	control	VERB
ejde-1401	162	27	mean	mean	ADJ
ejde-1401	162	28	curvature	curvature	NOUN
ejde-1401	162	29	(	(	PUNCT
ejde-1401	162	30	see	see	VERB
ejde-1401	162	31	[	[	X
ejde-1401	162	32	20	20	NUM
ejde-1401	162	33	,	,	PUNCT
ejde-1401	162	34	example	example	NOUN
ejde-1401	162	35	1.14	1.14	NUM
ejde-1401	162	36	]	]	PUNCT
ejde-1401	162	37	)	)	PUNCT
ejde-1401	162	38	.	.	PUNCT
ejde-1401	163	1	in	in	ADP
ejde-1401	163	2	particular	particular	ADJ
ejde-1401	163	3	,	,	PUNCT
ejde-1401	163	4	it	it	PRON
ejde-1401	163	5	holds	hold	VERB
ejde-1401	163	6	for	for	ADP
ejde-1401	163	7	every	every	DET
ejde-1401	163	8	constant	constant	ADJ
ejde-1401	163	9	mean	mean	ADJ
ejde-1401	163	10	curvature	curvature	NOUN
ejde-1401	163	11	hypersurface	hypersurface	NOUN
ejde-1401	163	12	properly	properly	ADV
ejde-1401	163	13	immersed	immerse	VERB
ejde-1401	163	14	into	into	ADP
ejde-1401	163	15	a	a	DET
ejde-1401	163	16	riemannian	riemannian	ADJ
ejde-1401	163	17	space	space	NOUN
ejde-1401	163	18	form	form	NOUN
ejde-1401	163	19	.	.	PUNCT
ejde-1401	164	1	more	more	ADV
ejde-1401	164	2	generally	generally	ADV
ejde-1401	164	3	,	,	PUNCT
ejde-1401	164	4	following	follow	VERB
ejde-1401	164	5	again	again	ADV
ejde-1401	164	6	the	the	DET
ejde-1401	164	7	terminology	terminology	NOUN
ejde-1401	164	8	introduced	introduce	VERB
ejde-1401	164	9	in	in	ADP
ejde-1401	164	10	[	[	X
ejde-1401	164	11	20	20	NUM
ejde-1401	164	12	]	]	PUNCT
ejde-1401	164	13	,	,	PUNCT
ejde-1401	164	14	the	the	DET
ejde-1401	164	15	weak	weak	ADJ
ejde-1401	164	16	omori	omori	NOUN
ejde-1401	164	17	-	-	PUNCT
ejde-1401	164	18	yau	yau	PROPN
ejde-1401	164	19	’s	’s	PART
ejde-1401	164	20	maximum	maximum	ADJ
ejde-1401	164	21	principle	principle	NOUN
ejde-1401	164	22	is	be	AUX
ejde-1401	164	23	said	say	VERB
ejde-1401	164	24	to	to	PART
ejde-1401	164	25	hold	hold	VERB
ejde-1401	164	26	on	on	ADP
ejde-1401	164	27	a	a	DET
ejde-1401	164	28	(	(	PUNCT
ejde-1401	164	29	not	not	PART
ejde-1401	164	30	necessarily	necessarily	ADV
ejde-1401	164	31	complete	complete	ADJ
ejde-1401	164	32	)	)	PUNCT
ejde-1401	164	33	n	n	CCONJ
ejde-1401	164	34	-	-	PUNCT
ejde-1401	164	35	dimensional	dimensional	ADJ
ejde-1401	164	36	riemannian	riemannian	ADJ
ejde-1401	164	37	manifold	manifold	NOUN
ejde-1401	164	38	(	(	PUNCT
ejde-1401	164	39	σn	σn	PROPN
ejde-1401	164	40	,	,	PUNCT
ejde-1401	164	41	g	g	NOUN
ejde-1401	164	42	)	)	PUNCT
ejde-1401	164	43	if	if	SCONJ
ejde-1401	164	44	,	,	PUNCT
ejde-1401	164	45	for	for	ADP
ejde-1401	164	46	any	any	DET
ejde-1401	164	47	smooth	smooth	ADJ
ejde-1401	164	48	function	function	NOUN
ejde-1401	164	49	u	u	PROPN
ejde-1401	164	50	∈	∈	PROPN
ejde-1401	164	51	c2(σn	c2(σn	PROPN
ejde-1401	164	52	)	)	PUNCT
ejde-1401	164	53	with	with	ADP
ejde-1401	164	54	supς	supς	NOUN
ejde-1401	164	55	u	u	X
ejde-1401	164	56	<	<	X
ejde-1401	164	57	+	+	NOUN
ejde-1401	164	58	∞	∞	PROPN
ejde-1401	164	59	,	,	PUNCT
ejde-1401	164	60	there	there	PRON
ejde-1401	164	61	exists	exist	VERB
ejde-1401	164	62	a	a	DET
ejde-1401	164	63	sequence	sequence	NOUN
ejde-1401	164	64	of	of	ADP
ejde-1401	164	65	points	point	NOUN
ejde-1401	164	66	(	(	PUNCT
ejde-1401	164	67	pk	pk	NOUN
ejde-1401	164	68	)	)	PUNCT
ejde-1401	164	69	⊂	⊂	PROPN
ejde-1401	164	70	σn	σn	NOUN
ejde-1401	164	71	with	with	ADP
ejde-1401	164	72	the	the	DET
ejde-1401	164	73	properties	property	NOUN
ejde-1401	164	74	lim	lim	PROPN
ejde-1401	164	75	k	k	PROPN
ejde-1401	164	76	u(pk	u(pk	PROPN
ejde-1401	164	77	)	)	PUNCT
ejde-1401	164	78	=	=	SYM
ejde-1401	164	79	sup	sup	NOUN
ejde-1401	164	80	σ	σ	NUM
ejde-1401	164	81	u	u	PROPN
ejde-1401	164	82	and	and	CCONJ
ejde-1401	164	83	lim	lim	PROPN
ejde-1401	164	84	sup	sup	PROPN
ejde-1401	164	85	k	k	PROPN
ejde-1401	164	86	∆u(pk	∆u(pk	ADV
ejde-1401	164	87	)	)	PUNCT
ejde-1401	164	88	≤	≤	NOUN
ejde-1401	164	89	0	0	NUM
ejde-1401	164	90	.	.	PUNCT
ejde-1401	165	1	in	in	ADP
ejde-1401	165	2	this	this	DET
ejde-1401	165	3	setting	setting	NOUN
ejde-1401	165	4	,	,	PUNCT
ejde-1401	165	5	pigola	pigola	PROPN
ejde-1401	165	6	,	,	PUNCT
ejde-1401	165	7	rigoli	rigoli	NOUN
ejde-1401	165	8	and	and	CCONJ
ejde-1401	165	9	setti	setti	NOUN
ejde-1401	165	10	[	[	X
ejde-1401	165	11	19	19	NUM
ejde-1401	165	12	,	,	PUNCT
ejde-1401	165	13	20	20	NUM
ejde-1401	165	14	]	]	PUNCT
ejde-1401	165	15	proved	prove	VERB
ejde-1401	165	16	the	the	DET
ejde-1401	165	17	following	following	ADJ
ejde-1401	165	18	equivalence	equivalence	NOUN
ejde-1401	165	19	:	:	PUNCT
ejde-1401	165	20	lemma	lemma	PROPN
ejde-1401	165	21	3.11	3.11	NUM
ejde-1401	165	22	.	.	PUNCT
ejde-1401	166	1	a	a	DET
ejde-1401	166	2	riemannian	riemannian	ADJ
ejde-1401	166	3	manifold	manifold	NOUN
ejde-1401	166	4	(	(	PUNCT
ejde-1401	166	5	σn	σn	PROPN
ejde-1401	166	6	,	,	PUNCT
ejde-1401	166	7	g	g	NOUN
ejde-1401	166	8	)	)	PUNCT
ejde-1401	166	9	is	be	AUX
ejde-1401	166	10	stochastically	stochastically	ADV
ejde-1401	166	11	complete	complete	ADJ
ejde-1401	166	12	if	if	SCONJ
ejde-1401	167	1	and	and	CCONJ
ejde-1401	167	2	only	only	ADV
ejde-1401	167	3	if	if	SCONJ
ejde-1401	167	4	the	the	DET
ejde-1401	167	5	weak	weak	ADJ
ejde-1401	167	6	omori	omori	NOUN
ejde-1401	167	7	-	-	PUNCT
ejde-1401	167	8	yau	yau	PROPN
ejde-1401	167	9	’s	’s	PART
ejde-1401	167	10	maximum	maximum	ADJ
ejde-1401	167	11	principle	principle	NOUN
ejde-1401	167	12	holds	hold	VERB
ejde-1401	167	13	on	on	ADP
ejde-1401	167	14	(	(	PUNCT
ejde-1401	167	15	σn	σn	NOUN
ejde-1401	167	16	,	,	PUNCT
ejde-1401	167	17	g	g	NOUN
ejde-1401	167	18	)	)	PUNCT
ejde-1401	167	19	.	.	PUNCT
ejde-1401	168	1	with	with	ADP
ejde-1401	168	2	this	this	DET
ejde-1401	168	3	previous	previous	ADJ
ejde-1401	168	4	discussion	discussion	NOUN
ejde-1401	168	5	in	in	ADP
ejde-1401	168	6	mind	mind	NOUN
ejde-1401	168	7	,	,	PUNCT
ejde-1401	168	8	we	we	PRON
ejde-1401	168	9	are	be	AUX
ejde-1401	168	10	able	able	ADJ
ejde-1401	168	11	to	to	PART
ejde-1401	168	12	present	present	VERB
ejde-1401	168	13	our	our	PRON
ejde-1401	168	14	next	next	ADJ
ejde-1401	168	15	characterization	characterization	NOUN
ejde-1401	168	16	result	result	NOUN
ejde-1401	168	17	.	.	PUNCT
ejde-1401	169	1	theorem	theorem	VERB
ejde-1401	169	2	3.12	3.12	NUM
ejde-1401	169	3	.	.	PUNCT
ejde-1401	170	1	let	let	AUX
ejde-1401	170	2	(	(	PUNCT
ejde-1401	170	3	σn	σn	NOUN
ejde-1401	170	4	,	,	PUNCT
ejde-1401	170	5	g	g	NOUN
ejde-1401	170	6	,	,	PUNCT
ejde-1401	170	7	u	u	NOUN
ejde-1401	170	8	)	)	PUNCT
ejde-1401	170	9	be	be	VERB
ejde-1401	170	10	a	a	DET
ejde-1401	170	11	stochastically	stochastically	ADV
ejde-1401	170	12	complete	complete	ADJ
ejde-1401	170	13	m	m	NOUN
ejde-1401	170	14	-	-	PUNCT
ejde-1401	170	15	quasi	quasi	ADJ
ejde-1401	170	16	yamabe	yamabe	PROPN
ejde-1401	170	17	gradient	gradient	PROPN
ejde-1401	170	18	soliton	soliton	NOUN
ejde-1401	170	19	whose	whose	DET
ejde-1401	170	20	ricci	ricci	PROPN
ejde-1401	170	21	tensor	tensor	NOUN
ejde-1401	170	22	satisfies	satisfie	NOUN
ejde-1401	170	23	ric(∇u,∇u	ric(∇u,∇u	PROPN
ejde-1401	170	24	)	)	PUNCT
ejde-1401	170	25	≤	≤	PROPN
ejde-1401	170	26	−α|∇u|2	−α|∇u|2	NUM
ejde-1401	170	27	,	,	PUNCT
ejde-1401	170	28	for	for	ADP
ejde-1401	170	29	some	some	DET
ejde-1401	170	30	positive	positive	ADJ
ejde-1401	170	31	constant	constant	ADJ
ejde-1401	170	32	α	α	PROPN
ejde-1401	170	33	∈	∈	PROPN
ejde-1401	170	34	r.	r.	NOUN
ejde-1401	170	35	if	if	SCONJ
ejde-1401	170	36	|∇u|	|∇u|	PROPN
ejde-1401	170	37	∈	∈	PROPN
ejde-1401	170	38	l∞(σ	l∞(σ	NOUN
ejde-1401	170	39	)	)	PUNCT
ejde-1401	170	40	,	,	PUNCT
ejde-1401	170	41	then	then	ADV
ejde-1401	170	42	(	(	PUNCT
ejde-1401	170	43	σn	σn	PROPN
ejde-1401	170	44	,	,	PUNCT
ejde-1401	170	45	g	g	NOUN
ejde-1401	170	46	,	,	PUNCT
ejde-1401	170	47	u	u	NOUN
ejde-1401	170	48	)	)	PUNCT
ejde-1401	170	49	is	be	AUX
ejde-1401	170	50	trivial	trivial	ADJ
ejde-1401	170	51	and	and	CCONJ
ejde-1401	170	52	r	r	NOUN
ejde-1401	170	53	=	=	SYM
ejde-1401	170	54	ρ	ρ	PROPN
ejde-1401	170	55	on	on	ADP
ejde-1401	170	56	σn	σn	PROPN
ejde-1401	170	57	.	.	PUNCT
ejde-1401	171	1	proof	proof	NOUN
ejde-1401	171	2	.	.	PUNCT
ejde-1401	172	1	initially	initially	ADV
ejde-1401	172	2	,	,	PUNCT
ejde-1401	172	3	we	we	PRON
ejde-1401	172	4	recall	recall	VERB
ejde-1401	172	5	that	that	SCONJ
ejde-1401	172	6	1	1	NUM
ejde-1401	172	7	2	2	NUM
ejde-1401	172	8	∆|∇u|2	∆|∇u|2	NOUN
ejde-1401	172	9	=	=	SYM
ejde-1401	172	10	|∇u|∆|∇u|+	|∇u|∆|∇u|+	X
ejde-1401	172	11	g(∇|∇u|,∇|∇u|	g(∇|∇u|,∇|∇u|	NOUN
ejde-1401	172	12	)	)	PUNCT
ejde-1401	172	13	.	.	PUNCT
ejde-1401	173	1	now	now	ADV
ejde-1401	173	2	,	,	PUNCT
ejde-1401	173	3	applying	apply	VERB
ejde-1401	173	4	once	once	ADV
ejde-1401	173	5	more	more	ADJ
ejde-1401	173	6	kato	kato	PROPN
ejde-1401	173	7	’s	’s	PART
ejde-1401	173	8	inequality	inequality	NOUN
ejde-1401	173	9	,	,	PUNCT
ejde-1401	173	10	from	from	ADP
ejde-1401	173	11	(	(	PUNCT
ejde-1401	173	12	2.10	2.10	NUM
ejde-1401	173	13	)	)	PUNCT
ejde-1401	173	14	we	we	PRON
ejde-1401	173	15	obtain	obtain	VERB
ejde-1401	173	16	|∇u|∆|∇u|+	|∇u|∆|∇u|+	NOUN
ejde-1401	173	17	g(∇|∇u|,∇|∇u|	g(∇|∇u|,∇|∇u|	NOUN
ejde-1401	173	18	)	)	PUNCT
ejde-1401	174	1	=	=	PUNCT
ejde-1401	174	2	|∇2u|2	|∇2u|2	PRON
ejde-1401	174	3	−	−	NUM
ejde-1401	174	4	1	1	NUM
ejde-1401	174	5	n−	n−	NOUN
ejde-1401	174	6	1	1	NUM
ejde-1401	174	7	ric(∇u,∇u	ric(∇u,∇u	PROPN
ejde-1401	174	8	)	)	PUNCT
ejde-1401	174	9	≥	≥	NOUN
ejde-1401	174	10	|∇|∇u||2	|∇|∇u||2	PROPN
ejde-1401	174	11	−	−	PROPN
ejde-1401	174	12	1	1	NUM
ejde-1401	174	13	n−	n−	NOUN
ejde-1401	174	14	1	1	NUM
ejde-1401	174	15	ric(∇u,∇u	ric(∇u,∇u	NOUN
ejde-1401	174	16	)	)	PUNCT
ejde-1401	174	17	.	.	PUNCT
ejde-1401	175	1	since	since	SCONJ
ejde-1401	175	2	|∇|∇u||2	|∇|∇u||2	PROPN
ejde-1401	175	3	=	=	SYM
ejde-1401	175	4	g(∇|∇u|,∇|∇u|	g(∇|∇u|,∇|∇u|	X
ejde-1401	175	5	)	)	PUNCT
ejde-1401	175	6	,	,	PUNCT
ejde-1401	175	7	from	from	ADP
ejde-1401	175	8	above	above	ADP
ejde-1401	175	9	inequality	inequality	NOUN
ejde-1401	175	10	we	we	PRON
ejde-1401	175	11	obtain	obtain	VERB
ejde-1401	175	12	|∇u|∆|∇u|	|∇u|∆|∇u|	NUM
ejde-1401	175	13	≥	≥	NOUN
ejde-1401	175	14	−	−	NOUN
ejde-1401	175	15	1	1	NUM
ejde-1401	175	16	n−	n−	NOUN
ejde-1401	175	17	1	1	NUM
ejde-1401	175	18	ric(∇u,∇u	ric(∇u,∇u	PROPN
ejde-1401	175	19	)	)	PUNCT
ejde-1401	175	20	≥	≥	NOUN
ejde-1401	175	21	α	α	PRON
ejde-1401	175	22	n−	n−	NOUN
ejde-1401	175	23	1	1	NUM
ejde-1401	175	24	|∇u|2	|∇u|2	NOUN
ejde-1401	175	25	,	,	PUNCT
ejde-1401	175	26	where	where	SCONJ
ejde-1401	175	27	it	it	PRON
ejde-1401	175	28	was	be	AUX
ejde-1401	175	29	used	use	VERB
ejde-1401	175	30	the	the	DET
ejde-1401	175	31	hypothesis	hypothesis	NOUN
ejde-1401	175	32	on	on	ADP
ejde-1401	175	33	ric(∇u,∇u	ric(∇u,∇u	PROPN
ejde-1401	175	34	)	)	PUNCT
ejde-1401	175	35	in	in	ADP
ejde-1401	175	36	the	the	DET
ejde-1401	175	37	last	last	ADJ
ejde-1401	175	38	inequality	inequality	NOUN
ejde-1401	175	39	.	.	PUNCT
ejde-1401	176	1	supposing	suppose	VERB
ejde-1401	176	2	that	that	DET
ejde-1401	176	3	supς	supς	NOUN
ejde-1401	176	4	|∇u|	|∇u|	PROPN
ejde-1401	176	5	>	>	X
ejde-1401	176	6	0	0	PUNCT
ejde-1401	176	7	and	and	CCONJ
ejde-1401	176	8	taking	take	VERB
ejde-1401	176	9	into	into	ADP
ejde-1401	176	10	account	account	NOUN
ejde-1401	176	11	that	that	DET
ejde-1401	176	12	|∇u|	|∇u|	ADJ
ejde-1401	176	13	∈	∈	PROPN
ejde-1401	176	14	l∞(σn	l∞(σn	NOUN
ejde-1401	176	15	)	)	PUNCT
ejde-1401	177	1	we	we	PRON
ejde-1401	177	2	can	can	AUX
ejde-1401	177	3	apply	apply	VERB
ejde-1401	177	4	the	the	DET
ejde-1401	177	5	lemma	lemma	PROPN
ejde-1401	177	6	3.11	3.11	NUM
ejde-1401	177	7	to	to	PART
ejde-1401	177	8	obtain	obtain	VERB
ejde-1401	177	9	0	0	NUM
ejde-1401	177	10	≥	≥	NOUN
ejde-1401	177	11	lim	lim	PROPN
ejde-1401	177	12	sup	sup	PROPN
ejde-1401	177	13	k	k	PROPN
ejde-1401	177	14	∆|∇u|	∆|∇u|	PROPN
ejde-1401	177	15	≥	≥	NUM
ejde-1401	177	16	α	α	PRON
ejde-1401	177	17	n−	n−	NOUN
ejde-1401	177	18	1	1	NUM
ejde-1401	177	19	sup	sup	NOUN
ejde-1401	177	20	σ	σ	PROPN
ejde-1401	177	21	|∇u|	|∇u|	PROPN
ejde-1401	177	22	>	>	X
ejde-1401	177	23	0	0	NUM
ejde-1401	177	24	,	,	PUNCT
ejde-1401	177	25	which	which	PRON
ejde-1401	177	26	is	be	AUX
ejde-1401	177	27	a	a	DET
ejde-1401	177	28	contradiction	contradiction	NOUN
ejde-1401	177	29	.	.	PUNCT
ejde-1401	178	1	so	so	ADV
ejde-1401	178	2	,	,	PUNCT
ejde-1401	178	3	we	we	PRON
ejde-1401	178	4	conclude	conclude	VERB
ejde-1401	178	5	that	that	DET
ejde-1401	178	6	supς	supς	NOUN
ejde-1401	178	7	|∇u|	|∇u|	ADJ
ejde-1401	178	8	=	=	SYM
ejde-1401	178	9	0	0	PUNCT
ejde-1401	179	1	and	and	CCONJ
ejde-1401	179	2	,	,	PUNCT
ejde-1401	179	3	therefore	therefore	ADV
ejde-1401	179	4	,	,	PUNCT
ejde-1401	179	5	u	u	NOUN
ejde-1401	179	6	is	be	AUX
ejde-1401	179	7	constant	constant	ADJ
ejde-1401	179	8	.	.	PUNCT
ejde-1401	180	1	to	to	PART
ejde-1401	180	2	finish	finish	VERB
ejde-1401	180	3	the	the	DET
ejde-1401	180	4	proof	proof	NOUN
ejde-1401	180	5	we	we	PRON
ejde-1401	180	6	observe	observe	VERB
ejde-1401	180	7	that	that	SCONJ
ejde-1401	180	8	(	(	PUNCT
ejde-1401	180	9	2.2	2.2	NUM
ejde-1401	180	10	)	)	PUNCT
ejde-1401	180	11	gives	give	VERB
ejde-1401	180	12	n	n	PRON
ejde-1401	180	13	m2	m2	PROPN
ejde-1401	180	14	(	(	PUNCT
ejde-1401	180	15	r−	r−	PROPN
ejde-1401	180	16	ρ)2u2	ρ)2u2	PROPN
ejde-1401	180	17	=	=	SYM
ejde-1401	180	18	0	0	PUNCT
ejde-1401	181	1	and	and	CCONJ
ejde-1401	181	2	,	,	PUNCT
ejde-1401	181	3	consequently	consequently	ADV
ejde-1401	181	4	,	,	PUNCT
ejde-1401	181	5	r	r	NOUN
ejde-1401	181	6	=	=	SYM
ejde-1401	181	7	ρ	ρ	PROPN
ejde-1401	181	8	.	.	PUNCT
ejde-1401	182	1	□	□	SYM
ejde-1401	182	2	8	8	NUM
ejde-1401	182	3	g.	g.	PROPN
ejde-1401	182	4	molica	molica	PROPN
ejde-1401	182	5	bisci	bisci	PROPN
ejde-1401	182	6	,	,	PUNCT
ejde-1401	182	7	h.	h.	PROPN
ejde-1401	182	8	f.	f.	PROPN
ejde-1401	182	9	de	de	PROPN
ejde-1401	182	10	lima	lima	PROPN
ejde-1401	182	11	,	,	PUNCT
ejde-1401	182	12	a.	a.	PROPN
ejde-1401	182	13	v.	v.	PROPN
ejde-1401	182	14	f.	f.	PROPN
ejde-1401	182	15	leite	leite	PROPN
ejde-1401	182	16	,	,	PUNCT
ejde-1401	182	17	m.	m.	NOUN
ejde-1401	182	18	a.	a.	PROPN
ejde-1401	182	19	l.	l.	PROPN
ejde-1401	182	20	velásquez	velásquez	PROPN
ejde-1401	182	21	ejde-2025/62	ejde-2025/62	PROPN
ejde-1401	182	22	we	we	PRON
ejde-1401	182	23	recall	recall	VERB
ejde-1401	182	24	that	that	SCONJ
ejde-1401	182	25	a	a	PRON
ejde-1401	182	26	(	(	PUNCT
ejde-1401	182	27	non	non	X
ejde-1401	182	28	necessarily	necessarily	ADV
ejde-1401	182	29	complete	complete	ADJ
ejde-1401	182	30	)	)	PUNCT
ejde-1401	182	31	riemannian	riemannian	ADJ
ejde-1401	182	32	manifold	manifold	NOUN
ejde-1401	182	33	(	(	PUNCT
ejde-1401	182	34	σn	σn	PROPN
ejde-1401	182	35	,	,	PUNCT
ejde-1401	182	36	g	g	NOUN
ejde-1401	182	37	)	)	PUNCT
ejde-1401	182	38	is	be	AUX
ejde-1401	182	39	called	call	VERB
ejde-1401	182	40	parabolic	parabolic	ADJ
ejde-1401	182	41	when	when	SCONJ
ejde-1401	182	42	the	the	DET
ejde-1401	182	43	only	only	ADJ
ejde-1401	182	44	subharmonic	subharmonic	ADJ
ejde-1401	182	45	functions	function	NOUN
ejde-1401	182	46	u	u	PROPN
ejde-1401	182	47	∈	∈	PROPN
ejde-1401	182	48	c∞(σn	c∞(σn	NOUN
ejde-1401	182	49	)	)	PUNCT
ejde-1401	182	50	which	which	PRON
ejde-1401	182	51	are	be	AUX
ejde-1401	182	52	bounded	bound	VERB
ejde-1401	182	53	from	from	ADP
ejde-1401	182	54	above	above	ADV
ejde-1401	182	55	are	be	AUX
ejde-1401	182	56	the	the	DET
ejde-1401	182	57	constant	constant	ADJ
ejde-1401	182	58	ones	one	NOUN
ejde-1401	182	59	.	.	PUNCT
ejde-1401	183	1	taking	take	VERB
ejde-1401	183	2	into	into	ADP
ejde-1401	183	3	account	account	NOUN
ejde-1401	183	4	[	[	X
ejde-1401	183	5	11	11	NUM
ejde-1401	183	6	,	,	PUNCT
ejde-1401	183	7	corollary	corollary	ADJ
ejde-1401	183	8	6.4	6.4	NUM
ejde-1401	183	9	]	]	PUNCT
ejde-1401	183	10	,	,	PUNCT
ejde-1401	183	11	we	we	PRON
ejde-1401	183	12	have	have	VERB
ejde-1401	183	13	that	that	SCONJ
ejde-1401	183	14	every	every	DET
ejde-1401	183	15	parabolic	parabolic	ADJ
ejde-1401	183	16	riemannian	riemannian	ADJ
ejde-1401	183	17	manifold	manifold	NOUN
ejde-1401	183	18	is	be	AUX
ejde-1401	183	19	stochastically	stochastically	ADV
ejde-1401	183	20	complete	complete	ADJ
ejde-1401	183	21	.	.	PUNCT
ejde-1401	184	1	in	in	ADP
ejde-1401	184	2	this	this	DET
ejde-1401	184	3	setting	setting	NOUN
ejde-1401	184	4	,	,	PUNCT
ejde-1401	184	5	we	we	PRON
ejde-1401	184	6	obtain	obtain	VERB
ejde-1401	184	7	the	the	DET
ejde-1401	184	8	following	follow	VERB
ejde-1401	184	9	consequence	consequence	NOUN
ejde-1401	184	10	of	of	ADP
ejde-1401	184	11	theorem	theorem	ADJ
ejde-1401	184	12	3.12	3.12	NUM
ejde-1401	184	13	.	.	PUNCT
ejde-1401	185	1	corollary	corollary	ADJ
ejde-1401	185	2	3.13	3.13	NUM
ejde-1401	185	3	.	.	PUNCT
ejde-1401	186	1	let	let	AUX
ejde-1401	186	2	(	(	PUNCT
ejde-1401	186	3	σn	σn	NOUN
ejde-1401	186	4	,	,	PUNCT
ejde-1401	186	5	g	g	NOUN
ejde-1401	186	6	,	,	PUNCT
ejde-1401	186	7	u	u	NOUN
ejde-1401	186	8	)	)	PUNCT
ejde-1401	186	9	be	be	AUX
ejde-1401	186	10	a	a	DET
ejde-1401	186	11	parabolic	parabolic	ADJ
ejde-1401	186	12	m	m	NOUN
ejde-1401	186	13	-	-	PUNCT
ejde-1401	186	14	quasi	quasi	ADJ
ejde-1401	186	15	yamabe	yamabe	PROPN
ejde-1401	186	16	gradient	gradient	PROPN
ejde-1401	186	17	soliton	soliton	NOUN
ejde-1401	186	18	whose	whose	DET
ejde-1401	186	19	ricci	ricci	PROPN
ejde-1401	186	20	tensor	tensor	NOUN
ejde-1401	186	21	satisfies	satisfie	NOUN
ejde-1401	186	22	ric(∇u,∇u	ric(∇u,∇u	PROPN
ejde-1401	186	23	)	)	PUNCT
ejde-1401	186	24	≤	≤	PROPN
ejde-1401	186	25	−α|∇u|2	−α|∇u|2	NUM
ejde-1401	186	26	,	,	PUNCT
ejde-1401	186	27	for	for	ADP
ejde-1401	186	28	some	some	DET
ejde-1401	186	29	positive	positive	ADJ
ejde-1401	186	30	constant	constant	ADJ
ejde-1401	186	31	α	α	PROPN
ejde-1401	186	32	∈	∈	PROPN
ejde-1401	186	33	r.	r.	NOUN
ejde-1401	186	34	if	if	SCONJ
ejde-1401	186	35	|∇u|	|∇u|	PROPN
ejde-1401	186	36	∈	∈	PROPN
ejde-1401	186	37	l∞(σ	l∞(σ	NOUN
ejde-1401	186	38	)	)	PUNCT
ejde-1401	186	39	,	,	PUNCT
ejde-1401	186	40	then	then	ADV
ejde-1401	186	41	(	(	PUNCT
ejde-1401	186	42	σn	σn	PROPN
ejde-1401	186	43	,	,	PUNCT
ejde-1401	186	44	g	g	NOUN
ejde-1401	186	45	,	,	PUNCT
ejde-1401	186	46	u	u	NOUN
ejde-1401	186	47	)	)	PUNCT
ejde-1401	186	48	is	be	AUX
ejde-1401	186	49	trivial	trivial	ADJ
ejde-1401	186	50	and	and	CCONJ
ejde-1401	186	51	r	r	NOUN
ejde-1401	186	52	=	=	SYM
ejde-1401	186	53	ρ	ρ	PROPN
ejde-1401	186	54	on	on	ADP
ejde-1401	186	55	σn	σn	NOUN
ejde-1401	186	56	.	.	PUNCT
ejde-1401	187	1	considering	consider	VERB
ejde-1401	187	2	[	[	X
ejde-1401	187	3	3	3	NUM
ejde-1401	187	4	,	,	PUNCT
ejde-1401	187	5	theorem	theorem	VERB
ejde-1401	187	6	2.13	2.13	NUM
ejde-1401	187	7	]	]	PUNCT
ejde-1401	187	8	we	we	PRON
ejde-1401	187	9	can	can	AUX
ejde-1401	187	10	establish	establish	VERB
ejde-1401	187	11	our	our	PRON
ejde-1401	187	12	second	second	ADJ
ejde-1401	187	13	corollary	corollary	NOUN
ejde-1401	187	14	of	of	ADP
ejde-1401	187	15	theorem	theorem	ADJ
ejde-1401	187	16	3.12	3.12	NUM
ejde-1401	187	17	.	.	PUNCT
ejde-1401	188	1	corollary	corollary	ADJ
ejde-1401	188	2	3.14	3.14	NUM
ejde-1401	188	3	.	.	PUNCT
ejde-1401	189	1	let	let	AUX
ejde-1401	189	2	(	(	PUNCT
ejde-1401	189	3	σn	σn	NOUN
ejde-1401	189	4	,	,	PUNCT
ejde-1401	189	5	g	g	NOUN
ejde-1401	189	6	,	,	PUNCT
ejde-1401	189	7	u	u	NOUN
ejde-1401	189	8	)	)	PUNCT
ejde-1401	189	9	be	be	AUX
ejde-1401	189	10	a	a	DET
ejde-1401	189	11	complete	complete	ADJ
ejde-1401	189	12	m	m	NOUN
ejde-1401	189	13	-	-	PUNCT
ejde-1401	189	14	quasi	quasi	ADJ
ejde-1401	189	15	yamabe	yamabe	PROPN
ejde-1401	189	16	gradient	gradient	PROPN
ejde-1401	189	17	soliton	soliton	NOUN
ejde-1401	189	18	whose	whose	DET
ejde-1401	189	19	ricci	ricci	PROPN
ejde-1401	189	20	tensor	tensor	NOUN
ejde-1401	189	21	satisfies	satisfie	NOUN
ejde-1401	189	22	ric(∇u,∇u	ric(∇u,∇u	PROPN
ejde-1401	189	23	)	)	PUNCT
ejde-1401	189	24	≤	≤	PROPN
ejde-1401	189	25	−α|∇u|2	−α|∇u|2	NUM
ejde-1401	189	26	,	,	PUNCT
ejde-1401	189	27	for	for	ADP
ejde-1401	189	28	some	some	DET
ejde-1401	189	29	positive	positive	ADJ
ejde-1401	189	30	constant	constant	ADJ
ejde-1401	189	31	α	α	NOUN
ejde-1401	189	32	∈	∈	NOUN
ejde-1401	189	33	r	r	NOUN
ejde-1401	189	34	and	and	CCONJ
ejde-1401	189	35	ric	ric	PROPN
ejde-1401	189	36	≥	≥	PROPN
ejde-1401	189	37	−g(r	−g(r	PROPN
ejde-1401	189	38	)	)	PUNCT
ejde-1401	189	39	,	,	PUNCT
ejde-1401	189	40	where	where	SCONJ
ejde-1401	189	41	r	r	NOUN
ejde-1401	189	42	denotes	denote	VERB
ejde-1401	189	43	the	the	DET
ejde-1401	189	44	riemannian	riemannian	ADJ
ejde-1401	189	45	distance	distance	NOUN
ejde-1401	189	46	function	function	NOUN
ejde-1401	189	47	from	from	ADP
ejde-1401	189	48	a	a	DET
ejde-1401	189	49	fixed	fix	VERB
ejde-1401	189	50	origin	origin	NOUN
ejde-1401	189	51	in	in	ADP
ejde-1401	189	52	σn	σn	NOUN
ejde-1401	189	53	and	and	CCONJ
ejde-1401	189	54	the	the	DET
ejde-1401	189	55	function	function	NOUN
ejde-1401	189	56	g	g	PROPN
ejde-1401	189	57	∈	∈	PROPN
ejde-1401	189	58	c1([0,+∞	c1([0,+∞	PROPN
ejde-1401	189	59	)	)	PUNCT
ejde-1401	189	60	)	)	PUNCT
ejde-1401	189	61	satisfies	satisfie	NOUN
ejde-1401	189	62	g(0	g(0	NOUN
ejde-1401	189	63	)	)	PUNCT
ejde-1401	189	64	>	>	X
ejde-1401	189	65	0	0	NUM
ejde-1401	189	66	,	,	PUNCT
ejde-1401	189	67	g′(0	g′(0	PROPN
ejde-1401	189	68	)	)	PUNCT
ejde-1401	189	69	≥	≥	NOUN
ejde-1401	189	70	0	0	NUM
ejde-1401	189	71	and	and	CCONJ
ejde-1401	189	72	g−	g−	ADJ
ejde-1401	189	73	1	1	NUM
ejde-1401	189	74	2	2	NUM
ejde-1401	189	75	/∈	/∈	CCONJ
ejde-1401	189	76	l1([0,+∞	l1([0,+∞	PROPN
ejde-1401	189	77	)	)	PUNCT
ejde-1401	189	78	)	)	PUNCT
ejde-1401	189	79	.	.	PUNCT
ejde-1401	190	1	if	if	SCONJ
ejde-1401	190	2	|∇u|	|∇u|	PROPN
ejde-1401	190	3	∈	∈	PROPN
ejde-1401	190	4	l∞(σ	l∞(σ	NOUN
ejde-1401	190	5	)	)	PUNCT
ejde-1401	190	6	,	,	PUNCT
ejde-1401	190	7	then	then	ADV
ejde-1401	190	8	(	(	PUNCT
ejde-1401	190	9	σn	σn	PROPN
ejde-1401	190	10	,	,	PUNCT
ejde-1401	190	11	g	g	NOUN
ejde-1401	190	12	,	,	PUNCT
ejde-1401	190	13	u	u	NOUN
ejde-1401	190	14	)	)	PUNCT
ejde-1401	190	15	is	be	AUX
ejde-1401	190	16	trivial	trivial	ADJ
ejde-1401	190	17	and	and	CCONJ
ejde-1401	190	18	r	r	NOUN
ejde-1401	190	19	=	=	SYM
ejde-1401	190	20	ρ	ρ	PROPN
ejde-1401	190	21	on	on	ADP
ejde-1401	190	22	σn	σn	PROPN
ejde-1401	190	23	.	.	PROPN
ejde-1401	190	24	3.4	3.4	NUM
ejde-1401	190	25	.	.	PUNCT
ejde-1401	190	26	via	via	ADP
ejde-1401	190	27	convergence	convergence	NOUN
ejde-1401	190	28	at	at	ADP
ejde-1401	190	29	infinity	infinity	NOUN
ejde-1401	190	30	.	.	PUNCT
ejde-1401	191	1	for	for	ADP
ejde-1401	191	2	our	our	PRON
ejde-1401	191	3	last	last	ADJ
ejde-1401	191	4	result	result	NOUN
ejde-1401	191	5	,	,	PUNCT
ejde-1401	191	6	we	we	PRON
ejde-1401	191	7	need	need	VERB
ejde-1401	191	8	the	the	DET
ejde-1401	191	9	concept	concept	NOUN
ejde-1401	191	10	to	to	PART
ejde-1401	191	11	convergence	convergence	VERB
ejde-1401	191	12	to	to	ADP
ejde-1401	191	13	zero	zero	NUM
ejde-1401	191	14	at	at	ADP
ejde-1401	191	15	infinity	infinity	NOUN
ejde-1401	191	16	.	.	PUNCT
ejde-1401	192	1	given	give	VERB
ejde-1401	192	2	a	a	DET
ejde-1401	192	3	(	(	PUNCT
ejde-1401	192	4	connected	connected	ADJ
ejde-1401	192	5	)	)	PUNCT
ejde-1401	192	6	complete	complete	ADJ
ejde-1401	192	7	noncompact	noncompact	NOUN
ejde-1401	192	8	riemannian	riemannian	ADJ
ejde-1401	192	9	manifold	manifold	NOUN
ejde-1401	192	10	(	(	PUNCT
ejde-1401	192	11	σn	σn	PROPN
ejde-1401	192	12	,	,	PUNCT
ejde-1401	192	13	g	g	NOUN
ejde-1401	192	14	)	)	PUNCT
ejde-1401	192	15	and	and	CCONJ
ejde-1401	192	16	denoting	denote	VERB
ejde-1401	192	17	by	by	ADP
ejde-1401	192	18	d	d	PROPN
ejde-1401	192	19	(	(	PUNCT
ejde-1401	192	20	·	·	PUNCT
ejde-1401	192	21	,	,	PUNCT
ejde-1401	192	22	o	o	NOUN
ejde-1401	192	23	)	)	PUNCT
ejde-1401	192	24	:	:	PUNCT
ejde-1401	192	25	σn	σn	X
ejde-1401	192	26	→	→	PUNCT
ejde-1401	192	27	[	[	X
ejde-1401	192	28	0,+∞	0,+∞	NUM
ejde-1401	192	29	)	)	PUNCT
ejde-1401	192	30	the	the	DET
ejde-1401	192	31	riemannian	riemannian	ADJ
ejde-1401	192	32	distance	distance	NOUN
ejde-1401	192	33	of	of	ADP
ejde-1401	192	34	σn	σn	NOUN
ejde-1401	192	35	measured	measure	VERB
ejde-1401	192	36	from	from	ADP
ejde-1401	192	37	a	a	DET
ejde-1401	192	38	fixed	fix	VERB
ejde-1401	192	39	point	point	NOUN
ejde-1401	192	40	o	o	X
ejde-1401	192	41	∈	∈	PROPN
ejde-1401	192	42	σn	σn	PROPN
ejde-1401	192	43	,	,	PUNCT
ejde-1401	192	44	a	a	DET
ejde-1401	192	45	function	function	NOUN
ejde-1401	192	46	h	h	NOUN
ejde-1401	192	47	∈	∈	PROPN
ejde-1401	192	48	c∞(σn	c∞(σn	NOUN
ejde-1401	192	49	)	)	PUNCT
ejde-1401	192	50	converges	converge	VERB
ejde-1401	192	51	to	to	ADP
ejde-1401	192	52	zero	zero	NUM
ejde-1401	192	53	at	at	ADP
ejde-1401	192	54	infinity	infinity	NOUN
ejde-1401	192	55	when	when	SCONJ
ejde-1401	192	56	lim	lim	PROPN
ejde-1401	192	57	d(x	d(x	PROPN
ejde-1401	192	58	,	,	PUNCT
ejde-1401	192	59	o)→∞	o)→∞	ADJ
ejde-1401	192	60	h(x	h(x	PROPN
ejde-1401	192	61	)	)	PUNCT
ejde-1401	192	62	=	=	PUNCT
ejde-1401	193	1	0	0	X
ejde-1401	193	2	.	.	PUNCT
ejde-1401	194	1	the	the	DET
ejde-1401	194	2	following	follow	VERB
ejde-1401	194	3	lemma	lemma	PROPN
ejde-1401	194	4	is	be	AUX
ejde-1401	194	5	due	due	ADJ
ejde-1401	194	6	to	to	ADP
ejde-1401	194	7	aĺıas	aĺıa	NOUN
ejde-1401	194	8	,	,	PUNCT
ejde-1401	194	9	caminha	caminha	NOUN
ejde-1401	194	10	and	and	CCONJ
ejde-1401	194	11	do	do	VERB
ejde-1401	194	12	nascimento	nascimento	PROPN
ejde-1401	195	1	[	[	X
ejde-1401	195	2	1	1	NUM
ejde-1401	195	3	]	]	PUNCT
ejde-1401	195	4	.	.	PUNCT
ejde-1401	196	1	lemma	lemma	PROPN
ejde-1401	196	2	3.15	3.15	NUM
ejde-1401	196	3	.	.	PUNCT
ejde-1401	197	1	let	let	AUX
ejde-1401	197	2	(	(	PUNCT
ejde-1401	197	3	σn	σn	NOUN
ejde-1401	197	4	,	,	PUNCT
ejde-1401	197	5	g	g	NOUN
ejde-1401	197	6	)	)	PUNCT
ejde-1401	197	7	be	be	AUX
ejde-1401	197	8	a	a	DET
ejde-1401	197	9	complete	complete	ADJ
ejde-1401	197	10	noncompact	noncompact	NOUN
ejde-1401	197	11	riemannian	riemannian	NOUN
ejde-1401	197	12	manifold	manifold	NOUN
ejde-1401	197	13	and	and	CCONJ
ejde-1401	197	14	let	let	VERB
ejde-1401	197	15	x	x	PROPN
ejde-1401	197	16	∈	∈	PROPN
ejde-1401	197	17	x(σn	x(σn	PROPN
ejde-1401	197	18	)	)	PUNCT
ejde-1401	197	19	be	be	VERB
ejde-1401	197	20	a	a	DET
ejde-1401	197	21	smooth	smooth	ADJ
ejde-1401	197	22	vector	vector	NOUN
ejde-1401	197	23	field	field	NOUN
ejde-1401	197	24	on	on	ADP
ejde-1401	197	25	σn	σn	PROPN
ejde-1401	197	26	.	.	PROPN
ejde-1401	197	27	assume	assume	VERB
ejde-1401	197	28	that	that	SCONJ
ejde-1401	197	29	there	there	PRON
ejde-1401	197	30	exists	exist	VERB
ejde-1401	197	31	a	a	DET
ejde-1401	197	32	nonnegative	nonnegative	ADJ
ejde-1401	197	33	,	,	PUNCT
ejde-1401	197	34	non	non	ADJ
ejde-1401	197	35	-	-	ADJ
ejde-1401	197	36	identically	identically	ADV
ejde-1401	197	37	vanishing	vanish	VERB
ejde-1401	197	38	function	function	NOUN
ejde-1401	197	39	v	v	ADP
ejde-1401	197	40	∈	∈	PROPN
ejde-1401	197	41	c∞(m	c∞(m	NOUN
ejde-1401	197	42	)	)	PUNCT
ejde-1401	197	43	which	which	PRON
ejde-1401	197	44	converges	converge	VERB
ejde-1401	197	45	to	to	ADP
ejde-1401	197	46	zero	zero	NUM
ejde-1401	197	47	at	at	ADP
ejde-1401	197	48	infinity	infinity	NOUN
ejde-1401	197	49	and	and	CCONJ
ejde-1401	197	50	such	such	ADJ
ejde-1401	197	51	that	that	SCONJ
ejde-1401	197	52	g(∇v	g(∇v	NOUN
ejde-1401	197	53	,	,	PUNCT
ejde-1401	197	54	x	x	X
ejde-1401	197	55	)	)	PUNCT
ejde-1401	197	56	≥	≥	NOUN
ejde-1401	197	57	0	0	NUM
ejde-1401	197	58	.	.	PUNCT
ejde-1401	198	1	if	if	SCONJ
ejde-1401	198	2	divg	divg	NOUN
ejde-1401	198	3	x	x	SYM
ejde-1401	198	4	≥	≥	NOUN
ejde-1401	198	5	0	0	NUM
ejde-1401	198	6	on	on	ADP
ejde-1401	198	7	σn	σn	PROPN
ejde-1401	198	8	,	,	PUNCT
ejde-1401	198	9	then	then	ADV
ejde-1401	198	10	g(∇v	g(∇v	NUM
ejde-1401	198	11	,	,	PUNCT
ejde-1401	198	12	x	x	NOUN
ejde-1401	198	13	)	)	PUNCT
ejde-1401	198	14	≡	≡	PROPN
ejde-1401	198	15	0	0	NUM
ejde-1401	198	16	on	on	ADP
ejde-1401	198	17	σn	σn	PROPN
ejde-1401	198	18	.	.	PUNCT
ejde-1401	199	1	we	we	PRON
ejde-1401	199	2	close	close	VERB
ejde-1401	199	3	our	our	PRON
ejde-1401	199	4	paper	paper	NOUN
ejde-1401	199	5	with	with	ADP
ejde-1401	199	6	the	the	DET
ejde-1401	199	7	following	follow	VERB
ejde-1401	199	8	characterization	characterization	NOUN
ejde-1401	199	9	result	result	NOUN
ejde-1401	199	10	.	.	PUNCT
ejde-1401	200	1	theorem	theorem	VERB
ejde-1401	200	2	3.16	3.16	NUM
ejde-1401	200	3	.	.	PUNCT
ejde-1401	201	1	let	let	AUX
ejde-1401	201	2	(	(	PUNCT
ejde-1401	201	3	σn	σn	NOUN
ejde-1401	201	4	,	,	PUNCT
ejde-1401	201	5	g	g	NOUN
ejde-1401	201	6	,	,	PUNCT
ejde-1401	201	7	u	u	NOUN
ejde-1401	201	8	)	)	PUNCT
ejde-1401	201	9	be	be	AUX
ejde-1401	201	10	a	a	DET
ejde-1401	201	11	complete	complete	ADJ
ejde-1401	201	12	noncompact	noncompact	NOUN
ejde-1401	201	13	m	m	NOUN
ejde-1401	201	14	-	-	PUNCT
ejde-1401	201	15	quasi	quasi	ADJ
ejde-1401	201	16	yamabe	yamabe	PROPN
ejde-1401	201	17	gradient	gradient	PROPN
ejde-1401	201	18	soliton	soliton	NOUN
ejde-1401	201	19	whose	whose	DET
ejde-1401	201	20	ricci	ricci	PROPN
ejde-1401	201	21	tensor	tensor	NOUN
ejde-1401	201	22	satisfies	satisfie	NOUN
ejde-1401	201	23	ric(∇u,∇u	ric(∇u,∇u	PROPN
ejde-1401	201	24	)	)	PUNCT
ejde-1401	201	25	≤	≤	NOUN
ejde-1401	201	26	0	0	NUM
ejde-1401	201	27	.	.	PUNCT
ejde-1401	202	1	if	if	SCONJ
ejde-1401	202	2	|∇u|	|∇u|	ADJ
ejde-1401	202	3	converges	converge	NOUN
ejde-1401	202	4	to	to	ADP
ejde-1401	202	5	zero	zero	NUM
ejde-1401	202	6	at	at	ADP
ejde-1401	202	7	infinity	infinity	NOUN
ejde-1401	202	8	,	,	PUNCT
ejde-1401	202	9	then	then	ADV
ejde-1401	202	10	(	(	PUNCT
ejde-1401	202	11	σn	σn	PROPN
ejde-1401	202	12	,	,	PUNCT
ejde-1401	202	13	g	g	NOUN
ejde-1401	202	14	,	,	PUNCT
ejde-1401	202	15	u	u	NOUN
ejde-1401	202	16	)	)	PUNCT
ejde-1401	202	17	is	be	AUX
ejde-1401	202	18	trivial	trivial	ADJ
ejde-1401	202	19	and	and	CCONJ
ejde-1401	202	20	r	r	NOUN
ejde-1401	202	21	=	=	SYM
ejde-1401	202	22	ρ	ρ	PROPN
ejde-1401	202	23	on	on	ADP
ejde-1401	202	24	σn	σn	PROPN
ejde-1401	202	25	.	.	PUNCT
ejde-1401	203	1	proof	proof	NOUN
ejde-1401	203	2	.	.	PUNCT
ejde-1401	204	1	suppose	suppose	VERB
ejde-1401	204	2	by	by	ADP
ejde-1401	204	3	contradiction	contradiction	NOUN
ejde-1401	204	4	that	that	PRON
ejde-1401	204	5	(	(	PUNCT
ejde-1401	204	6	σn	σn	PROPN
ejde-1401	204	7	,	,	PUNCT
ejde-1401	204	8	g	g	NOUN
ejde-1401	204	9	,	,	PUNCT
ejde-1401	204	10	u	u	NOUN
ejde-1401	204	11	)	)	PUNCT
ejde-1401	204	12	is	be	AUX
ejde-1401	204	13	not	not	PART
ejde-1401	204	14	a	a	DET
ejde-1401	204	15	trivial	trivial	ADJ
ejde-1401	204	16	m	m	NOUN
ejde-1401	204	17	-	-	PUNCT
ejde-1401	204	18	quasi	quasi	ADJ
ejde-1401	204	19	yamabe	yamabe	PROPN
ejde-1401	204	20	gradient	gradient	PROPN
ejde-1401	204	21	soliton	soliton	NOUN
ejde-1401	204	22	.	.	PUNCT
ejde-1401	205	1	since	since	SCONJ
ejde-1401	205	2	we	we	PRON
ejde-1401	205	3	are	be	AUX
ejde-1401	205	4	supposing	suppose	VERB
ejde-1401	205	5	that	that	SCONJ
ejde-1401	205	6	ric(∇u,∇u	ric(∇u,∇u	NOUN
ejde-1401	205	7	)	)	PUNCT
ejde-1401	205	8	≤	≤	NOUN
ejde-1401	205	9	0	0	NUM
ejde-1401	205	10	,	,	PUNCT
ejde-1401	205	11	taking	take	VERB
ejde-1401	205	12	the	the	DET
ejde-1401	205	13	smooth	smooth	ADJ
ejde-1401	205	14	vector	vector	NOUN
ejde-1401	205	15	fieldx	fieldx	NOUN
ejde-1401	205	16	=	=	PUNCT
ejde-1401	205	17	∇|∇u|2	∇|∇u|2	PROPN
ejde-1401	205	18	∈	∈	PROPN
ejde-1401	205	19	x(σn	x(σn	PROPN
ejde-1401	205	20	)	)	PUNCT
ejde-1401	205	21	we	we	PRON
ejde-1401	205	22	have	have	VERB
ejde-1401	205	23	that	that	DET
ejde-1401	205	24	divg	divg	NOUN
ejde-1401	205	25	x	x	PUNCT
ejde-1401	206	1	=	=	PUNCT
ejde-1401	206	2	∆|∇u|2	∆|∇u|2	NOUN
ejde-1401	206	3	≥	≥	NOUN
ejde-1401	206	4	0	0	NUM
ejde-1401	206	5	.	.	PUNCT
ejde-1401	207	1	furthermore	furthermore	ADV
ejde-1401	207	2	,	,	PUNCT
ejde-1401	207	3	taking	take	VERB
ejde-1401	207	4	v	v	NOUN
ejde-1401	207	5	:	:	PUNCT
ejde-1401	207	6	=	=	SYM
ejde-1401	207	7	|∇u|2	|∇u|2	NOUN
ejde-1401	207	8	we	we	PRON
ejde-1401	207	9	observe	observe	VERB
ejde-1401	207	10	that	that	SCONJ
ejde-1401	207	11	v	v	NOUN
ejde-1401	207	12	is	be	AUX
ejde-1401	207	13	a	a	DET
ejde-1401	207	14	nonnegative	nonnegative	ADJ
ejde-1401	207	15	and	and	CCONJ
ejde-1401	207	16	non	non	ADJ
ejde-1401	207	17	-	-	ADJ
ejde-1401	207	18	identically	identically	ADV
ejde-1401	207	19	vanishing	vanish	VERB
ejde-1401	207	20	smooth	smooth	ADJ
ejde-1401	207	21	function	function	NOUN
ejde-1401	207	22	of	of	ADP
ejde-1401	207	23	c∞(σn	c∞(σn	NOUN
ejde-1401	207	24	)	)	PUNCT
ejde-1401	207	25	.	.	PUNCT
ejde-1401	208	1	on	on	ADP
ejde-1401	208	2	the	the	DET
ejde-1401	208	3	other	other	ADJ
ejde-1401	208	4	hand	hand	NOUN
ejde-1401	208	5	,	,	PUNCT
ejde-1401	208	6	we	we	PRON
ejde-1401	208	7	obtain	obtain	VERB
ejde-1401	208	8	g(x,∇v	g(x,∇v	PROPN
ejde-1401	208	9	)	)	PUNCT
ejde-1401	208	10	=	=	SYM
ejde-1401	208	11	g(∇|∇u|2,∇|∇u|2	g(∇|∇u|2,∇|∇u|2	PROPN
ejde-1401	208	12	)	)	PUNCT
ejde-1401	208	13	≥	≥	NOUN
ejde-1401	208	14	0	0	NUM
ejde-1401	208	15	.	.	PUNCT
ejde-1401	209	1	so	so	ADV
ejde-1401	209	2	,	,	PUNCT
ejde-1401	209	3	applying	apply	VERB
ejde-1401	209	4	lemma	lemma	PROPN
ejde-1401	209	5	3.15	3.15	NUM
ejde-1401	209	6	we	we	PRON
ejde-1401	209	7	conclude	conclude	VERB
ejde-1401	209	8	that	that	PRON
ejde-1401	209	9	g(∇|∇u|2,∇|∇u|2	g(∇|∇u|2,∇|∇u|2	PROPN
ejde-1401	209	10	)	)	PUNCT
ejde-1401	209	11	=	=	SYM
ejde-1401	209	12	0	0	PUNCT
ejde-1401	210	1	and	and	CCONJ
ejde-1401	210	2	,	,	PUNCT
ejde-1401	210	3	consequently	consequently	ADV
ejde-1401	210	4	,	,	PUNCT
ejde-1401	210	5	|∇u|	|∇u|	ADJ
ejde-1401	210	6	is	be	AUX
ejde-1401	210	7	constant	constant	ADJ
ejde-1401	210	8	.	.	PUNCT
ejde-1401	211	1	since	since	SCONJ
ejde-1401	211	2	|∇u|	|∇u|	ADJ
ejde-1401	211	3	converges	converge	NOUN
ejde-1401	211	4	to	to	ADP
ejde-1401	211	5	zero	zero	NUM
ejde-1401	211	6	at	at	ADP
ejde-1401	211	7	infinity	infinity	NOUN
ejde-1401	211	8	,	,	PUNCT
ejde-1401	211	9	we	we	PRON
ejde-1401	211	10	have	have	VERB
ejde-1401	211	11	that	that	PRON
ejde-1401	211	12	|∇u|	|∇u|	ADJ
ejde-1401	211	13	=	=	SYM
ejde-1401	211	14	0	0	PUNCT
ejde-1401	212	1	and	and	CCONJ
ejde-1401	212	2	,	,	PUNCT
ejde-1401	212	3	therefore	therefore	ADV
ejde-1401	212	4	,	,	PUNCT
ejde-1401	212	5	u	u	NOUN
ejde-1401	212	6	is	be	AUX
ejde-1401	212	7	constant	constant	ADJ
ejde-1401	212	8	,	,	PUNCT
ejde-1401	212	9	which	which	PRON
ejde-1401	212	10	is	be	AUX
ejde-1401	212	11	an	an	DET
ejde-1401	212	12	absurd	absurd	ADJ
ejde-1401	212	13	.	.	PUNCT
ejde-1401	213	1	in	in	ADP
ejde-1401	213	2	this	this	DET
ejde-1401	213	3	picture	picture	NOUN
ejde-1401	213	4	,	,	PUNCT
ejde-1401	213	5	we	we	PRON
ejde-1401	213	6	have	have	AUX
ejde-1401	213	7	verified	verify	VERB
ejde-1401	213	8	that	that	SCONJ
ejde-1401	213	9	(	(	PUNCT
ejde-1401	213	10	σn	σn	PROPN
ejde-1401	213	11	,	,	PUNCT
ejde-1401	213	12	g	g	NOUN
ejde-1401	213	13	,	,	PUNCT
ejde-1401	213	14	u	u	NOUN
ejde-1401	213	15	)	)	PUNCT
ejde-1401	213	16	must	must	AUX
ejde-1401	213	17	be	be	AUX
ejde-1401	213	18	a	a	DET
ejde-1401	213	19	trivial	trivial	ADJ
ejde-1401	213	20	m	m	NOUN
ejde-1401	213	21	-	-	PUNCT
ejde-1401	213	22	quasi	quasi	ADJ
ejde-1401	213	23	yamabe	yamabe	PROPN
ejde-1401	213	24	gradient	gradient	PROPN
ejde-1401	213	25	soliton	soliton	NOUN
ejde-1401	213	26	.	.	PUNCT
ejde-1401	214	1	in	in	ADP
ejde-1401	214	2	particular	particular	ADJ
ejde-1401	214	3	,	,	PUNCT
ejde-1401	214	4	as	as	ADP
ejde-1401	214	5	before	before	ADV
ejde-1401	214	6	,	,	PUNCT
ejde-1401	214	7	we	we	PRON
ejde-1401	214	8	have	have	VERB
ejde-1401	214	9	0	0	NUM
ejde-1401	214	10	=	=	SYM
ejde-1401	214	11	∆|∇u|2	∆|∇u|2	PROPN
ejde-1401	214	12	≥	≥	NUM
ejde-1401	214	13	n	n	PRON
ejde-1401	214	14	m2	m2	PROPN
ejde-1401	214	15	(	(	PUNCT
ejde-1401	214	16	r−	r−	PROPN
ejde-1401	214	17	ρ)2u2	ρ)2u2	PROPN
ejde-1401	214	18	≥	≥	NOUN
ejde-1401	214	19	0	0	NUM
ejde-1401	214	20	.	.	PUNCT
ejde-1401	215	1	hence	hence	ADV
ejde-1401	215	2	,	,	PUNCT
ejde-1401	215	3	since	since	SCONJ
ejde-1401	215	4	u	u	PROPN
ejde-1401	215	5	>	>	X
ejde-1401	215	6	0	0	NUM
ejde-1401	215	7	,	,	PUNCT
ejde-1401	215	8	we	we	PRON
ejde-1401	215	9	also	also	ADV
ejde-1401	215	10	conclude	conclude	VERB
ejde-1401	215	11	that	that	SCONJ
ejde-1401	215	12	r	r	NOUN
ejde-1401	215	13	=	=	SYM
ejde-1401	215	14	ρ	ρ	PROPN
ejde-1401	215	15	.	.	PUNCT
ejde-1401	215	16	□	□	PUNCT
ejde-1401	215	17	remark	remark	NOUN
ejde-1401	215	18	3.17	3.17	NUM
ejde-1401	215	19	.	.	PUNCT
ejde-1401	216	1	let	let	VERB
ejde-1401	216	2	us	we	PRON
ejde-1401	216	3	consider	consider	VERB
ejde-1401	216	4	the	the	DET
ejde-1401	216	5	euclidean	euclidean	NOUN
ejde-1401	216	6	subset	subset	VERB
ejde-1401	216	7	σn	σn	NOUN
ejde-1401	216	8	:	:	PUNCT
ejde-1401	216	9	=	=	SYM
ejde-1401	216	10	{	{	PUNCT
ejde-1401	216	11	(	(	PUNCT
ejde-1401	216	12	x1	x1	PROPN
ejde-1401	216	13	,	,	PUNCT
ejde-1401	216	14	.	.	PUNCT
ejde-1401	216	15	.	.	PUNCT
ejde-1401	217	1	.	.	PUNCT
ejde-1401	218	1	,	,	PUNCT
ejde-1401	218	2	xn	xn	X
ejde-1401	218	3	)	)	PUNCT
ejde-1401	218	4	∈	∈	NOUN
ejde-1401	218	5	rn;x1	rn;x1	NOUN
ejde-1401	218	6	+	+	CCONJ
ejde-1401	218	7	·	·	PUNCT
ejde-1401	218	8	·	·	PUNCT
ejde-1401	218	9	·	·	PUNCT
ejde-1401	219	1	+	+	NUM
ejde-1401	219	2	xn	xn	PROPN
ejde-1401	219	3	>	>	X
ejde-1401	219	4	0	0	NUM
ejde-1401	219	5	}	}	PUNCT
ejde-1401	219	6	endowed	endow	VERB
ejde-1401	219	7	with	with	ADP
ejde-1401	219	8	the	the	DET
ejde-1401	219	9	euclidean	euclidean	ADJ
ejde-1401	219	10	metric	metric	ADJ
ejde-1401	219	11	gij	gij	NOUN
ejde-1401	219	12	=	=	SYM
ejde-1401	219	13	δij	δij	NOUN
ejde-1401	219	14	and	and	CCONJ
ejde-1401	219	15	potential	potential	ADJ
ejde-1401	219	16	function	function	NOUN
ejde-1401	219	17	f	f	PROPN
ejde-1401	219	18	defined	define	VERB
ejde-1401	219	19	by	by	ADP
ejde-1401	219	20	f(x1	f(x1	NOUN
ejde-1401	219	21	,	,	PUNCT
ejde-1401	219	22	.	.	PUNCT
ejde-1401	219	23	.	.	PUNCT
ejde-1401	220	1	.	.	PUNCT
ejde-1401	221	1	,	,	PUNCT
ejde-1401	221	2	xn	xn	X
ejde-1401	221	3	)	)	PUNCT
ejde-1401	222	1	=	=	PUNCT
ejde-1401	222	2	−m	−m	PROPN
ejde-1401	222	3	log(x1	log(x1	PROPN
ejde-1401	222	4	+	+	CCONJ
ejde-1401	222	5	·	·	PUNCT
ejde-1401	222	6	·	·	PUNCT
ejde-1401	222	7	·	·	PUNCT
ejde-1401	222	8	+	+	NUM
ejde-1401	222	9	xn	xn	NUM
ejde-1401	222	10	)	)	PUNCT
ejde-1401	222	11	.	.	PUNCT
ejde-1401	223	1	ejde-2025/62	ejde-2025/62	ADJ
ejde-1401	223	2	complete	complete	ADJ
ejde-1401	223	3	m	m	NOUN
ejde-1401	223	4	-	-	PUNCT
ejde-1401	223	5	quasi	quasi	ADJ
ejde-1401	223	6	yamabe	yamabe	PROPN
ejde-1401	223	7	gradient	gradient	PROPN
ejde-1401	223	8	solitons	soliton	NOUN
ejde-1401	223	9	9	9	NUM
ejde-1401	223	10	we	we	PRON
ejde-1401	223	11	have	have	VERB
ejde-1401	223	12	that	that	PRON
ejde-1401	223	13	(	(	PUNCT
ejde-1401	223	14	σn	σn	PROPN
ejde-1401	223	15	,	,	PUNCT
ejde-1401	223	16	g	g	NOUN
ejde-1401	223	17	)	)	PUNCT
ejde-1401	223	18	is	be	AUX
ejde-1401	223	19	ricci	ricci	NOUN
ejde-1401	223	20	-	-	PUNCT
ejde-1401	223	21	flat	flat	ADJ
ejde-1401	223	22	and	and	CCONJ
ejde-1401	223	23	∇2f	∇2f	NUM
ejde-1401	223	24	=	=	SYM
ejde-1401	223	25	1	1	NUM
ejde-1401	223	26	m∇f	m∇f	NOUN
ejde-1401	223	27	⊗	⊗	PROPN
ejde-1401	223	28	∇f	∇f	PROPN
ejde-1401	223	29	.	.	PUNCT
ejde-1401	224	1	in	in	ADP
ejde-1401	224	2	particular	particular	ADJ
ejde-1401	224	3	,	,	PUNCT
ejde-1401	224	4	taking	take	VERB
ejde-1401	224	5	u	u	NOUN
ejde-1401	224	6	=	=	PUNCT
ejde-1401	224	7	e−	e−	PROPN
ejde-1401	224	8	f	f	PROPN
ejde-1401	224	9	m	m	VERB
ejde-1401	224	10	,	,	PUNCT
ejde-1401	224	11	from	from	ADP
ejde-1401	224	12	(	(	PUNCT
ejde-1401	224	13	1.5	1.5	NUM
ejde-1401	224	14	)	)	PUNCT
ejde-1401	224	15	we	we	PRON
ejde-1401	224	16	deduce	deduce	VERB
ejde-1401	224	17	∇2u	∇2u	PROPN
ejde-1401	224	18	≡	≡	PROPN
ejde-1401	224	19	0	0	PUNCT
ejde-1401	224	20	.	.	PUNCT
ejde-1401	225	1	hence	hence	ADV
ejde-1401	225	2	,	,	PUNCT
ejde-1401	225	3	from	from	ADP
ejde-1401	225	4	(	(	PUNCT
ejde-1401	225	5	1.6	1.6	NUM
ejde-1401	225	6	)	)	PUNCT
ejde-1401	225	7	we	we	PRON
ejde-1401	225	8	have	have	VERB
ejde-1401	225	9	that	that	PRON
ejde-1401	225	10	(	(	PUNCT
ejde-1401	225	11	σn	σn	PROPN
ejde-1401	225	12	,	,	PUNCT
ejde-1401	225	13	g	g	NOUN
ejde-1401	225	14	,	,	PUNCT
ejde-1401	225	15	u	u	NOUN
ejde-1401	225	16	)	)	PUNCT
ejde-1401	225	17	is	be	AUX
ejde-1401	225	18	a	a	DET
ejde-1401	225	19	non	non	ADJ
ejde-1401	225	20	-	-	ADJ
ejde-1401	225	21	trivial	trivial	ADJ
ejde-1401	225	22	noncompact	noncompact	NOUN
ejde-1401	225	23	stochastically	stochastically	ADV
ejde-1401	225	24	complete	complete	ADJ
ejde-1401	225	25	m	m	NOUN
ejde-1401	225	26	-	-	PUNCT
ejde-1401	225	27	quasi	quasi	ADJ
ejde-1401	225	28	yamabe	yamabe	ADJ
ejde-1401	225	29	gradient	gradient	PROPN
ejde-1401	225	30	soliton	soliton	NOUN
ejde-1401	225	31	with	with	ADP
ejde-1401	225	32	ric	ric	PROPN
ejde-1401	225	33	≡	≡	PROPN
ejde-1401	225	34	0	0	PUNCT
ejde-1401	225	35	and	and	CCONJ
ejde-1401	225	36	such	such	ADJ
ejde-1401	225	37	that	that	DET
ejde-1401	225	38	ρ	ρ	NOUN
ejde-1401	225	39	=	=	SYM
ejde-1401	225	40	r	r	NOUN
ejde-1401	225	41	=	=	SYM
ejde-1401	225	42	0	0	NUM
ejde-1401	225	43	.	.	PUNCT
ejde-1401	226	1	therefore	therefore	ADV
ejde-1401	226	2	,	,	PUNCT
ejde-1401	226	3	through	through	ADP
ejde-1401	226	4	this	this	DET
ejde-1401	226	5	example	example	NOUN
ejde-1401	226	6	,	,	PUNCT
ejde-1401	226	7	we	we	PRON
ejde-1401	226	8	see	see	VERB
ejde-1401	226	9	the	the	DET
ejde-1401	226	10	importance	importance	NOUN
ejde-1401	226	11	of	of	ADP
ejde-1401	226	12	the	the	DET
ejde-1401	226	13	hypotheses	hypothesis	NOUN
ejde-1401	226	14	used	use	VERB
ejde-1401	226	15	to	to	PART
ejde-1401	226	16	establish	establish	VERB
ejde-1401	226	17	our	our	PRON
ejde-1401	226	18	triviality	triviality	NOUN
ejde-1401	226	19	results	result	NOUN
ejde-1401	226	20	.	.	PUNCT
ejde-1401	227	1	acknowledgements	acknowledgement	NOUN
ejde-1401	227	2	.	.	PUNCT
ejde-1401	228	1	this	this	DET
ejde-1401	228	2	work	work	NOUN
ejde-1401	228	3	was	be	AUX
ejde-1401	228	4	funded	fund	VERB
ejde-1401	228	5	by	by	ADP
ejde-1401	228	6	the	the	DET
ejde-1401	228	7	european	european	PROPN
ejde-1401	228	8	union	union	PROPN
ejde-1401	228	9	nextgenerationeu	nextgenerationeu	PROPN
ejde-1401	228	10	within	within	ADP
ejde-1401	228	11	the	the	DET
ejde-1401	228	12	framework	framework	NOUN
ejde-1401	228	13	of	of	ADP
ejde-1401	228	14	pnrr	pnrr	PROPN
ejde-1401	228	15	mission	mission	PROPN
ejde-1401	228	16	4	4	NUM
ejde-1401	228	17	component	component	NOUN
ejde-1401	228	18	2	2	NUM
ejde-1401	228	19	investment	investment	NOUN
ejde-1401	228	20	1.1	1.1	NUM
ejde-1401	228	21	under	under	ADP
ejde-1401	228	22	the	the	DET
ejde-1401	228	23	italian	italian	ADJ
ejde-1401	228	24	ministry	ministry	PROPN
ejde-1401	228	25	of	of	ADP
ejde-1401	228	26	university	university	PROPN
ejde-1401	228	27	and	and	CCONJ
ejde-1401	228	28	research	research	NOUN
ejde-1401	228	29	(	(	PUNCT
ejde-1401	228	30	mur	mur	NOUN
ejde-1401	228	31	)	)	PUNCT
ejde-1401	228	32	program	program	NOUN
ejde-1401	228	33	prin	prin	NOUN
ejde-1401	228	34	2022	2022	NUM
ejde-1401	228	35	grant	grant	NOUN
ejde-1401	228	36	number	number	NOUN
ejde-1401	228	37	2022bcfhn2	2022bcfhn2	NUM
ejde-1401	228	38	advanced	advanced	ADJ
ejde-1401	228	39	theoretical	theoretical	ADJ
ejde-1401	228	40	aspects	aspect	NOUN
ejde-1401	228	41	in	in	ADP
ejde-1401	228	42	pdes	pde	NOUN
ejde-1401	228	43	and	and	CCONJ
ejde-1401	228	44	their	their	PRON
ejde-1401	228	45	applications	application	NOUN
ejde-1401	228	46	cup	cup	NOUN
ejde-1401	228	47	:	:	PUNCT
ejde-1401	228	48	h53d23001960006	h53d23001960006	NOUN
ejde-1401	228	49	.	.	PUNCT
ejde-1401	229	1	g.	g.	PROPN
ejde-1401	229	2	molica	molica	PROPN
ejde-1401	229	3	bisci	bisci	PROPN
ejde-1401	229	4	was	be	AUX
ejde-1401	229	5	supported	support	VERB
ejde-1401	229	6	by	by	ADP
ejde-1401	229	7	indam	indam	ADJ
ejde-1401	229	8	-	-	PUNCT
ejde-1401	229	9	gnampa	gnampa	NOUN
ejde-1401	229	10	research	research	NOUN
ejde-1401	229	11	project	project	NOUN
ejde-1401	229	12	2024	2024	NUM
ejde-1401	229	13	:	:	PUNCT
ejde-1401	229	14	aspetti	aspetti	PROPN
ejde-1401	229	15	geometrici	geometrici	PROPN
ejde-1401	229	16	e	e	PROPN
ejde-1401	229	17	analitici	analitici	PROPN
ejde-1401	229	18	di	di	X
ejde-1401	229	19	alcuni	alcuni	PROPN
ejde-1401	229	20	problemi	problemi	X
ejde-1401	229	21	locali	locali	X
ejde-1401	229	22	e	e	X
ejde-1401	229	23	non	non	ADJ
ejde-1401	229	24	-	-	ADJ
ejde-1401	229	25	locali	locali	ADJ
ejde-1401	229	26	in	in	ADP
ejde-1401	229	27	mancanza	mancanza	PROPN
ejde-1401	229	28	di	di	PROPN
ejde-1401	229	29	compattezza	compattezza	PROPN
ejde-1401	229	30	cup	cup	PROPN
ejde-1401	229	31	e53c23001670001	e53c23001670001	PROPN
ejde-1401	229	32	.	.	PUNCT
ejde-1401	230	1	h.	h.	PROPN
ejde-1401	230	2	f.	f.	PROPN
ejde-1401	230	3	de	de	PROPN
ejde-1401	230	4	lima	lima	PROPN
ejde-1401	230	5	and	and	CCONJ
ejde-1401	230	6	a.	a.	NOUN
ejde-1401	230	7	l.	l.	PROPN
ejde-1401	230	8	velásquez	velásquez	PROPN
ejde-1401	230	9	were	be	AUX
ejde-1401	230	10	partially	partially	ADV
ejde-1401	230	11	supported	support	VERB
ejde-1401	230	12	by	by	ADP
ejde-1401	230	13	cnpq	cnpq	NOUN
ejde-1401	230	14	,	,	PUNCT
ejde-1401	230	15	brazil	brazil	PROPN
ejde-1401	230	16	,	,	PUNCT
ejde-1401	230	17	grants	grant	NOUN
ejde-1401	230	18	305608/2023	305608/2023	NUM
ejde-1401	230	19	-	-	SYM
ejde-1401	230	20	1	1	NUM
ejde-1401	230	21	and	and	CCONJ
ejde-1401	230	22	304891/2021	304891/2021	NUM
ejde-1401	230	23	-	-	SYM
ejde-1401	230	24	5	5	NUM
ejde-1401	230	25	,	,	PUNCT
ejde-1401	230	26	respectively	respectively	ADV
ejde-1401	230	27	.	.	PUNCT
ejde-1401	231	1	a.v	a.v	PROPN
ejde-1401	231	2	.	.	PROPN
ejde-1401	231	3	f.	f.	PROPN
ejde-1401	231	4	leite	leite	PROPN
ejde-1401	231	5	was	be	AUX
ejde-1401	231	6	supported	support	VERB
ejde-1401	231	7	by	by	ADP
ejde-1401	231	8	capes	cape	NOUN
ejde-1401	231	9	,	,	PUNCT
ejde-1401	231	10	brazil	brazil	PROPN
ejde-1401	231	11	.	.	PUNCT
ejde-1401	232	1	the	the	DET
ejde-1401	232	2	authors	author	NOUN
ejde-1401	232	3	would	would	AUX
ejde-1401	232	4	like	like	VERB
ejde-1401	232	5	to	to	PART
ejde-1401	232	6	thank	thank	VERB
ejde-1401	232	7	the	the	DET
ejde-1401	232	8	anonymous	anonymous	ADJ
ejde-1401	232	9	referee	referee	NOUN
ejde-1401	232	10	for	for	ADP
ejde-1401	232	11	his	his	PRON
ejde-1401	232	12	/	/	SYM
ejde-1401	232	13	her	her	PRON
ejde-1401	232	14	valuable	valuable	ADJ
ejde-1401	232	15	suggestions	suggestion	NOUN
ejde-1401	232	16	and	and	CCONJ
ejde-1401	232	17	useful	useful	ADJ
ejde-1401	232	18	comments	comment	NOUN
ejde-1401	232	19	which	which	PRON
ejde-1401	232	20	improved	improve	VERB
ejde-1401	232	21	the	the	DET
ejde-1401	232	22	paper	paper	NOUN
ejde-1401	232	23	.	.	PUNCT
ejde-1401	233	1	references	reference	NOUN
ejde-1401	233	2	[	[	X
ejde-1401	233	3	1	1	NUM
ejde-1401	233	4	]	]	PUNCT
ejde-1401	233	5	l.	l.	PROPN
ejde-1401	233	6	j.	j.	PROPN
ejde-1401	233	7	aĺıas	aĺıas	PROPN
ejde-1401	233	8	,	,	PUNCT
ejde-1401	233	9	a.	a.	NOUN
ejde-1401	233	10	caminha	caminha	NOUN
ejde-1401	233	11	,	,	PUNCT
ejde-1401	233	12	f.	f.	PROPN
ejde-1401	233	13	y.	y.	PROPN
ejde-1401	233	14	do	do	AUX
ejde-1401	233	15	nascimento	nascimento	PROPN
ejde-1401	233	16	;	;	PUNCT
ejde-1401	233	17	a	a	DET
ejde-1401	233	18	maximum	maximum	ADJ
ejde-1401	233	19	principle	principle	NOUN
ejde-1401	233	20	at	at	ADP
ejde-1401	233	21	infinity	infinity	NOUN
ejde-1401	233	22	with	with	ADP
ejde-1401	233	23	applications	application	NOUN
ejde-1401	233	24	to	to	ADP
ejde-1401	233	25	geometric	geometric	ADJ
ejde-1401	233	26	vector	vector	NOUN
ejde-1401	233	27	fields	field	NOUN
ejde-1401	233	28	,	,	PUNCT
ejde-1401	233	29	j.	j.	PROPN
ejde-1401	233	30	math	math	PROPN
ejde-1401	233	31	.	.	PUNCT
ejde-1401	234	1	anal	anal	PROPN
ejde-1401	234	2	.	.	PUNCT
ejde-1401	234	3	appl	appl	PROPN
ejde-1401	234	4	.	.	PROPN
ejde-1401	235	1	,	,	PUNCT
ejde-1401	235	2	474	474	NUM
ejde-1401	235	3	(	(	PUNCT
ejde-1401	235	4	2019	2019	NUM
ejde-1401	235	5	)	)	PUNCT
ejde-1401	235	6	,	,	PUNCT
ejde-1401	235	7	242–247	242–247	NUM
ejde-1401	235	8	.	.	PUNCT
ejde-1401	236	1	[	[	X
ejde-1401	236	2	2	2	NUM
ejde-1401	236	3	]	]	PUNCT
ejde-1401	236	4	l.	l.	PROPN
ejde-1401	236	5	j.	j.	PROPN
ejde-1401	236	6	aĺıas	aĺıas	PROPN
ejde-1401	236	7	,	,	PUNCT
ejde-1401	236	8	a.	a.	NOUN
ejde-1401	236	9	caminha	caminha	NOUN
ejde-1401	236	10	,	,	PUNCT
ejde-1401	236	11	f.	f.	PROPN
ejde-1401	236	12	y.	y.	PROPN
ejde-1401	236	13	do	do	AUX
ejde-1401	236	14	nascimento	nascimento	PROPN
ejde-1401	236	15	;	;	PUNCT
ejde-1401	236	16	a	a	DET
ejde-1401	236	17	maximum	maximum	ADJ
ejde-1401	236	18	principle	principle	NOUN
ejde-1401	236	19	related	relate	VERB
ejde-1401	236	20	to	to	ADP
ejde-1401	236	21	volume	volume	VERB
ejde-1401	236	22	growth	growth	NOUN
ejde-1401	236	23	and	and	CCONJ
ejde-1401	236	24	applications	application	NOUN
ejde-1401	236	25	,	,	PUNCT
ejde-1401	236	26	ann	ann	PROPN
ejde-1401	236	27	.	.	PROPN
ejde-1401	236	28	mat	mat	PROPN
ejde-1401	236	29	.	.	PUNCT
ejde-1401	236	30	pura	pura	NOUN
ejde-1401	236	31	appl	appl	PROPN
ejde-1401	236	32	.	.	PROPN
ejde-1401	236	33	,	,	PUNCT
ejde-1401	236	34	200	200	NUM
ejde-1401	236	35	(	(	PUNCT
ejde-1401	236	36	2021	2021	NUM
ejde-1401	236	37	)	)	PUNCT
ejde-1401	236	38	,	,	PUNCT
ejde-1401	236	39	1637–1650	1637–1650	NUM
ejde-1401	236	40	.	.	PUNCT
ejde-1401	237	1	[	[	X
ejde-1401	237	2	3	3	X
ejde-1401	237	3	]	]	X
ejde-1401	237	4	l.	l.	PROPN
ejde-1401	237	5	j.	j.	PROPN
ejde-1401	237	6	aĺıas	aĺıas	PROPN
ejde-1401	237	7	,	,	PUNCT
ejde-1401	237	8	p.	p.	PROPN
ejde-1401	237	9	mastrolia	mastrolia	PROPN
ejde-1401	237	10	,	,	PUNCT
ejde-1401	237	11	m	m	VERB
ejde-1401	237	12	do	do	VERB
ejde-1401	237	13	rigoli	rigoli	NOUN
ejde-1401	237	14	;	;	PUNCT
ejde-1401	237	15	maximum	maximum	ADJ
ejde-1401	237	16	principles	principle	NOUN
ejde-1401	237	17	and	and	CCONJ
ejde-1401	237	18	geometric	geometric	ADJ
ejde-1401	237	19	applications	application	NOUN
ejde-1401	237	20	,	,	PUNCT
ejde-1401	237	21	springer	springer	NOUN
ejde-1401	237	22	monographs	monograph	NOUN
ejde-1401	237	23	in	in	ADP
ejde-1401	237	24	mathematics	mathematic	NOUN
ejde-1401	237	25	,	,	PUNCT
ejde-1401	237	26	springer	springer	NOUN
ejde-1401	237	27	cham	cham	PROPN
ejde-1401	237	28	,	,	PUNCT
ejde-1401	237	29	new	new	PROPN
ejde-1401	237	30	york	york	PROPN
ejde-1401	237	31	,	,	PUNCT
ejde-1401	237	32	2016	2016	NUM
ejde-1401	237	33	.	.	PUNCT
ejde-1401	238	1	[	[	X
ejde-1401	238	2	4	4	X
ejde-1401	238	3	]	]	PUNCT
ejde-1401	238	4	t.	t.	PROPN
ejde-1401	238	5	aubin	aubin	PROPN
ejde-1401	238	6	;	;	PUNCT
ejde-1401	238	7	equations	equation	NOUN
ejde-1401	238	8	différentielles	différentielle	VERB
ejde-1401	238	9	non	non	NOUN
ejde-1401	238	10	linéaires	linéaire	NOUN
ejde-1401	238	11	et	et	PROPN
ejde-1401	238	12	problème	problème	PROPN
ejde-1401	238	13	de	de	PROPN
ejde-1401	238	14	yamabe	yamabe	PROPN
ejde-1401	238	15	concernant	concernant	PROPN
ejde-1401	238	16	la	la	PROPN
ejde-1401	238	17	courbure	courbure	PROPN
ejde-1401	238	18	scalaire	scalaire	NOUN
ejde-1401	238	19	,	,	PUNCT
ejde-1401	238	20	j.	j.	PROPN
ejde-1401	238	21	math	math	PROPN
ejde-1401	238	22	.	.	PUNCT
ejde-1401	239	1	pures	pure	NOUN
ejde-1401	239	2	appl	appl	PROPN
ejde-1401	239	3	.	.	PROPN
ejde-1401	239	4	,	,	PUNCT
ejde-1401	239	5	55	55	NUM
ejde-1401	239	6	(	(	PUNCT
ejde-1401	239	7	1976	1976	NUM
ejde-1401	239	8	)	)	PUNCT
ejde-1401	239	9	,	,	PUNCT
ejde-1401	239	10	269–296	269–296	NUM
ejde-1401	239	11	.	.	PUNCT
ejde-1401	240	1	[	[	X
ejde-1401	240	2	5	5	X
ejde-1401	240	3	]	]	PUNCT
ejde-1401	240	4	s.	s.	PROPN
ejde-1401	240	5	bochner	bochner	PROPN
ejde-1401	240	6	;	;	PUNCT
ejde-1401	240	7	vector	vector	NOUN
ejde-1401	240	8	fields	field	NOUN
ejde-1401	240	9	and	and	CCONJ
ejde-1401	240	10	ricci	ricci	PROPN
ejde-1401	240	11	curvature	curvature	PROPN
ejde-1401	240	12	,	,	PUNCT
ejde-1401	240	13	bull	bull	NOUN
ejde-1401	240	14	.	.	PUNCT
ejde-1401	240	15	am	be	AUX
ejde-1401	240	16	.	.	PUNCT
ejde-1401	241	1	math	math	NOUN
ejde-1401	241	2	.	.	PUNCT
ejde-1401	242	1	soc	soc	PROPN
ejde-1401	242	2	.	.	PUNCT
ejde-1401	242	3	,	,	PUNCT
ejde-1401	242	4	52	52	NUM
ejde-1401	242	5	(	(	PUNCT
ejde-1401	242	6	1946	1946	NUM
ejde-1401	242	7	)	)	PUNCT
ejde-1401	242	8	,	,	PUNCT
ejde-1401	242	9	776–797	776–797	NUM
ejde-1401	242	10	.	.	PUNCT
ejde-1401	243	1	[	[	X
ejde-1401	243	2	6	6	NUM
ejde-1401	243	3	]	]	PUNCT
ejde-1401	243	4	a.	a.	NOUN
ejde-1401	243	5	caminha	caminha	NOUN
ejde-1401	243	6	;	;	PUNCT
ejde-1401	243	7	the	the	DET
ejde-1401	243	8	geometry	geometry	NOUN
ejde-1401	243	9	of	of	ADP
ejde-1401	243	10	closed	close	VERB
ejde-1401	243	11	conformal	conformal	ADJ
ejde-1401	243	12	vector	vector	NOUN
ejde-1401	243	13	fields	field	NOUN
ejde-1401	243	14	on	on	ADP
ejde-1401	243	15	riemannian	riemannian	ADJ
ejde-1401	243	16	spaces	space	NOUN
ejde-1401	243	17	,	,	PUNCT
ejde-1401	243	18	bull	bull	PROPN
ejde-1401	243	19	.	.	PUNCT
ejde-1401	244	1	braz	braz	PROPN
ejde-1401	244	2	.	.	PUNCT
ejde-1401	244	3	math	math	PROPN
ejde-1401	244	4	.	.	PUNCT
ejde-1401	245	1	soc	soc	PROPN
ejde-1401	245	2	.	.	PUNCT
ejde-1401	245	3	,	,	PUNCT
ejde-1401	245	4	42	42	NUM
ejde-1401	245	5	(	(	PUNCT
ejde-1401	245	6	2011	2011	NUM
ejde-1401	245	7	)	)	PUNCT
ejde-1401	245	8	,	,	PUNCT
ejde-1401	245	9	277–300	277–300	NUM
ejde-1401	245	10	.	.	PUNCT
ejde-1401	246	1	[	[	X
ejde-1401	246	2	7	7	NUM
ejde-1401	246	3	]	]	X
ejde-1401	246	4	a.w	a.w	PROPN
ejde-1401	246	5	.	.	PROPN
ejde-1401	246	6	cunha	cunha	PROPN
ejde-1401	246	7	,	,	PUNCT
ejde-1401	246	8	e.	e.	PROPN
ejde-1401	246	9	l.	l.	PROPN
ejde-1401	246	10	de	de	PROPN
ejde-1401	246	11	lima	lima	PROPN
ejde-1401	246	12	,	,	PUNCT
ejde-1401	246	13	h.	h.	PROPN
ejde-1401	246	14	f.	f.	PROPN
ejde-1401	246	15	de	de	PROPN
ejde-1401	246	16	lima	lima	PROPN
ejde-1401	246	17	;	;	PUNCT
ejde-1401	246	18	applications	application	NOUN
ejde-1401	246	19	of	of	ADP
ejde-1401	246	20	certain	certain	ADJ
ejde-1401	246	21	maximum	maximum	ADJ
ejde-1401	246	22	principles	principle	NOUN
ejde-1401	246	23	to	to	PART
ejde-1401	246	24	gradient	gradient	VERB
ejde-1401	246	25	k	k	ADJ
ejde-1401	246	26	-	-	ADJ
ejde-1401	246	27	yamabe	yamabe	ADJ
ejde-1401	246	28	solitons	soliton	NOUN
ejde-1401	246	29	,	,	PUNCT
ejde-1401	246	30	boll	boll	NOUN
ejde-1401	246	31	.	.	PUNCT
ejde-1401	247	1	unione	unione	PROPN
ejde-1401	247	2	mat	mat	PROPN
ejde-1401	247	3	.	.	PUNCT
ejde-1401	247	4	ital	ital	PROPN
ejde-1401	247	5	.	.	PUNCT
ejde-1401	248	1	,17	,17	PUNCT
ejde-1401	248	2	(	(	PUNCT
ejde-1401	248	3	2024	2024	NUM
ejde-1401	248	4	)	)	PUNCT
ejde-1401	248	5	,	,	PUNCT
ejde-1401	248	6	759–766	759–766	NUM
ejde-1401	248	7	.	.	PUNCT
ejde-1401	249	1	[	[	X
ejde-1401	249	2	8	8	NUM
ejde-1401	249	3	]	]	X
ejde-1401	249	4	m.	m.	NOUN
ejde-1401	249	5	émery	émery	PROPN
ejde-1401	249	6	;	;	PUNCT
ejde-1401	249	7	stochastic	stochastic	ADJ
ejde-1401	249	8	calculus	calculus	NOUN
ejde-1401	249	9	on	on	ADP
ejde-1401	249	10	manifolds	manifold	NOUN
ejde-1401	249	11	,	,	PUNCT
ejde-1401	249	12	springer	springer	NOUN
ejde-1401	249	13	-	-	PUNCT
ejde-1401	249	14	verlag	verlag	PROPN
ejde-1401	249	15	,	,	PUNCT
ejde-1401	249	16	berlin	berlin	PROPN
ejde-1401	249	17	,	,	PUNCT
ejde-1401	249	18	1989	1989	NUM
ejde-1401	249	19	.	.	PUNCT
ejde-1401	250	1	[	[	X
ejde-1401	250	2	9	9	NUM
ejde-1401	250	3	]	]	PUNCT
ejde-1401	250	4	m.	m.	NOUN
ejde-1401	250	5	gaffney	gaffney	NOUN
ejde-1401	250	6	;	;	PUNCT
ejde-1401	250	7	a	a	DET
ejde-1401	250	8	special	special	ADJ
ejde-1401	250	9	stokes	stoke	NOUN
ejde-1401	250	10	’	'	PUNCT
ejde-1401	250	11	theorem	theorem	NOUN
ejde-1401	250	12	for	for	ADP
ejde-1401	250	13	complete	complete	ADJ
ejde-1401	250	14	riemannian	riemannian	ADJ
ejde-1401	250	15	manifolds	manifold	NOUN
ejde-1401	250	16	,	,	PUNCT
ejde-1401	250	17	ann	ann	PROPN
ejde-1401	250	18	.	.	PROPN
ejde-1401	250	19	of	of	ADP
ejde-1401	250	20	math	math	NOUN
ejde-1401	250	21	.	.	PUNCT
ejde-1401	250	22	,	,	PUNCT
ejde-1401	250	23	60	60	NUM
ejde-1401	250	24	(	(	PUNCT
ejde-1401	250	25	1954	1954	NUM
ejde-1401	250	26	)	)	PUNCT
ejde-1401	250	27	,	,	PUNCT
ejde-1401	250	28	140–145	140–145	NUM
ejde-1401	250	29	.	.	PUNCT
ejde-1401	251	1	[	[	X
ejde-1401	251	2	10	10	NUM
ejde-1401	251	3	]	]	X
ejde-1401	251	4	a.	a.	NOUN
ejde-1401	251	5	a.	a.	NOUN
ejde-1401	251	6	grigor’yan	grigor’yan	PROPN
ejde-1401	251	7	;	;	PUNCT
ejde-1401	251	8	stochastically	stochastically	ADV
ejde-1401	251	9	complete	complete	ADJ
ejde-1401	251	10	manifolds	manifold	NOUN
ejde-1401	251	11	and	and	CCONJ
ejde-1401	251	12	summable	summable	ADJ
ejde-1401	251	13	harmonic	harmonic	ADJ
ejde-1401	251	14	functions	function	NOUN
ejde-1401	251	15	,	,	PUNCT
ejde-1401	251	16	izv	izv	PROPN
ejde-1401	251	17	.	.	PROPN
ejde-1401	251	18	akad	akad	PROPN
ejde-1401	251	19	.	.	PUNCT
ejde-1401	252	1	nauk	nauk	PROPN
ejde-1401	252	2	sssr	sssr	PROPN
ejde-1401	252	3	ser	ser	PROPN
ejde-1401	252	4	.	.	PROPN
ejde-1401	253	1	mat	mat	PROPN
ejde-1401	253	2	.	.	PROPN
ejde-1401	253	3	,	,	PUNCT
ejde-1401	253	4	52	52	NUM
ejde-1401	253	5	(	(	PUNCT
ejde-1401	253	6	1988	1988	NUM
ejde-1401	253	7	)	)	PUNCT
ejde-1401	253	8	,	,	PUNCT
ejde-1401	253	9	1102–1108	1102–1108	NUM
ejde-1401	253	10	;	;	PUNCT
ejde-1401	253	11	translation	translation	NOUN
ejde-1401	253	12	in	in	ADP
ejde-1401	253	13	math	math	NOUN
ejde-1401	253	14	.	.	PUNCT
ejde-1401	254	1	ussr	ussr	PROPN
ejde-1401	254	2	-	-	PUNCT
ejde-1401	254	3	izv	izv	PROPN
ejde-1401	254	4	.	.	PROPN
ejde-1401	255	1	33	33	NUM
ejde-1401	255	2	(	(	PUNCT
ejde-1401	255	3	1989	1989	NUM
ejde-1401	255	4	)	)	PUNCT
ejde-1401	255	5	,	,	PUNCT
ejde-1401	256	1	425–432	425–432	NUM
ejde-1401	256	2	.	.	PUNCT
ejde-1401	257	1	[	[	X
ejde-1401	257	2	11	11	NUM
ejde-1401	257	3	]	]	PUNCT
ejde-1401	257	4	a.	a.	NOUN
ejde-1401	257	5	a.	a.	NOUN
ejde-1401	257	6	grigor’yan	grigor’yan	VERB
ejde-1401	257	7	;	;	PUNCT
ejde-1401	257	8	analytic	analytic	ADJ
ejde-1401	257	9	and	and	CCONJ
ejde-1401	257	10	geometric	geometric	ADJ
ejde-1401	257	11	background	background	NOUN
ejde-1401	257	12	of	of	ADP
ejde-1401	257	13	recurrence	recurrence	NOUN
ejde-1401	257	14	and	and	CCONJ
ejde-1401	257	15	non	non	ADJ
ejde-1401	257	16	-	-	NOUN
ejde-1401	257	17	explosion	explosion	NOUN
ejde-1401	257	18	of	of	ADP
ejde-1401	257	19	the	the	DET
ejde-1401	257	20	brownian	brownian	ADJ
ejde-1401	257	21	motion	motion	NOUN
ejde-1401	257	22	on	on	ADP
ejde-1401	257	23	riemannian	riemannian	ADJ
ejde-1401	257	24	manifolds	manifold	NOUN
ejde-1401	257	25	,	,	PUNCT
ejde-1401	257	26	bull	bull	NOUN
ejde-1401	257	27	.	.	PUNCT
ejde-1401	258	1	am	be	AUX
ejde-1401	258	2	.	.	PUNCT
ejde-1401	259	1	math	math	NOUN
ejde-1401	259	2	.	.	PUNCT
ejde-1401	260	1	soc	soc	PROPN
ejde-1401	260	2	.	.	PUNCT
ejde-1401	261	1	(	(	PUNCT
ejde-1401	261	2	n.s	n.s	PROPN
ejde-1401	261	3	.	.	PROPN
ejde-1401	261	4	)	)	PUNCT
ejde-1401	261	5	,	,	PUNCT
ejde-1401	261	6	36	36	NUM
ejde-1401	261	7	(	(	PUNCT
ejde-1401	261	8	1999	1999	NUM
ejde-1401	261	9	)	)	PUNCT
ejde-1401	261	10	,	,	PUNCT
ejde-1401	261	11	135–249	135–249	NUM
ejde-1401	261	12	.	.	PUNCT
ejde-1401	262	1	[	[	X
ejde-1401	262	2	12	12	NUM
ejde-1401	262	3	]	]	PUNCT
ejde-1401	262	4	r.	r.	PROPN
ejde-1401	262	5	hamilton	hamilton	PROPN
ejde-1401	262	6	,	,	PUNCT
ejde-1401	262	7	the	the	DET
ejde-1401	262	8	ricci	ricci	PROPN
ejde-1401	262	9	flow	flow	NOUN
ejde-1401	262	10	on	on	ADP
ejde-1401	262	11	surfaces	surface	NOUN
ejde-1401	262	12	;	;	PUNCT
ejde-1401	262	13	contemp	contemp	NOUN
ejde-1401	262	14	.	.	PUNCT
ejde-1401	263	1	math	math	NOUN
ejde-1401	263	2	.	.	PUNCT
ejde-1401	263	3	,	,	PUNCT
ejde-1401	263	4	71	71	NUM
ejde-1401	263	5	(	(	PUNCT
ejde-1401	263	6	1988	1988	NUM
ejde-1401	263	7	)	)	PUNCT
ejde-1401	263	8	,	,	PUNCT
ejde-1401	263	9	237–261	237–261	NUM
ejde-1401	263	10	.	.	PUNCT
ejde-1401	264	1	[	[	X
ejde-1401	264	2	13	13	NUM
ejde-1401	264	3	]	]	PUNCT
ejde-1401	264	4	s.	s.	PROPN
ejde-1401	264	5	y.	y.	PROPN
ejde-1401	264	6	hsu	hsu	PROPN
ejde-1401	264	7	;	;	PUNCT
ejde-1401	264	8	a	a	DET
ejde-1401	264	9	note	note	NOUN
ejde-1401	264	10	on	on	ADP
ejde-1401	264	11	compact	compact	ADJ
ejde-1401	264	12	gradient	gradient	ADJ
ejde-1401	264	13	yamabe	yamabe	ADJ
ejde-1401	264	14	solitons	soliton	NOUN
ejde-1401	264	15	,	,	PUNCT
ejde-1401	264	16	j.	j.	PROPN
ejde-1401	264	17	math	math	PROPN
ejde-1401	264	18	.	.	PUNCT
ejde-1401	265	1	anal	anal	PROPN
ejde-1401	265	2	.	.	PUNCT
ejde-1401	265	3	appl	appl	PROPN
ejde-1401	265	4	.	.	PROPN
ejde-1401	265	5	,	,	PUNCT
ejde-1401	265	6	388	388	NUM
ejde-1401	265	7	(	(	PUNCT
ejde-1401	265	8	2012	2012	NUM
ejde-1401	265	9	)	)	PUNCT
ejde-1401	265	10	,	,	PUNCT
ejde-1401	266	1	725–726	725–726	NUM
ejde-1401	266	2	.	.	PUNCT
ejde-1401	267	1	[	[	X
ejde-1401	267	2	14	14	NUM
ejde-1401	267	3	]	]	X
ejde-1401	267	4	g.	g.	PROPN
ejde-1401	267	5	huang	huang	PROPN
ejde-1401	267	6	,	,	PUNCT
ejde-1401	267	7	h.	h.	PROPN
ejde-1401	267	8	li	li	PROPN
ejde-1401	267	9	;	;	PUNCT
ejde-1401	267	10	on	on	ADP
ejde-1401	267	11	a	a	DET
ejde-1401	267	12	classification	classification	NOUN
ejde-1401	267	13	of	of	ADP
ejde-1401	267	14	the	the	DET
ejde-1401	267	15	quasi	quasi	ADJ
ejde-1401	267	16	yamabe	yamabe	PROPN
ejde-1401	267	17	gradient	gradient	PROPN
ejde-1401	267	18	solitons	soliton	NOUN
ejde-1401	267	19	,	,	PUNCT
ejde-1401	267	20	methods	method	NOUN
ejde-1401	267	21	appl	appl	NOUN
ejde-1401	267	22	.	.	PUNCT
ejde-1401	268	1	anal	anal	PROPN
ejde-1401	268	2	.	.	PROPN
ejde-1401	268	3	,	,	PUNCT
ejde-1401	268	4	21	21	NUM
ejde-1401	268	5	(	(	PUNCT
ejde-1401	268	6	2014	2014	NUM
ejde-1401	268	7	)	)	PUNCT
ejde-1401	268	8	,	,	PUNCT
ejde-1401	268	9	379–389	379–389	NUM
ejde-1401	268	10	.	.	PUNCT
ejde-1401	269	1	[	[	X
ejde-1401	269	2	15	15	NUM
ejde-1401	269	3	]	]	X
ejde-1401	269	4	j.	j.	PROPN
ejde-1401	269	5	m.	m.	PROPN
ejde-1401	269	6	lee	lee	PROPN
ejde-1401	269	7	,	,	PUNCT
ejde-1401	269	8	t.	t.	PROPN
ejde-1401	269	9	h.	h.	PROPN
ejde-1401	269	10	parker	parker	PROPN
ejde-1401	269	11	;	;	PUNCT
ejde-1401	269	12	the	the	DET
ejde-1401	269	13	yamabe	yamabe	ADJ
ejde-1401	269	14	problem	problem	NOUN
ejde-1401	269	15	,	,	PUNCT
ejde-1401	269	16	bull	bull	NOUN
ejde-1401	269	17	.	.	PUNCT
ejde-1401	270	1	amer	amer	PROPN
ejde-1401	270	2	.	.	PUNCT
ejde-1401	270	3	math	math	PROPN
ejde-1401	270	4	.	.	PUNCT
ejde-1401	271	1	soc	soc	PROPN
ejde-1401	271	2	.	.	PUNCT
ejde-1401	271	3	,	,	PUNCT
ejde-1401	271	4	17	17	NUM
ejde-1401	271	5	(	(	PUNCT
ejde-1401	271	6	1987	1987	NUM
ejde-1401	271	7	)	)	PUNCT
ejde-1401	271	8	,	,	PUNCT
ejde-1401	271	9	37–91	37–91	NUM
ejde-1401	271	10	.	.	PUNCT
ejde-1401	272	1	[	[	X
ejde-1401	272	2	16	16	NUM
ejde-1401	272	3	]	]	X
ejde-1401	272	4	d.	d.	PROPN
ejde-1401	272	5	m.	m.	PROPN
ejde-1401	272	6	naik	naik	PROPN
ejde-1401	272	7	;	;	PUNCT
ejde-1401	272	8	ricci	ricci	PROPN
ejde-1401	272	9	solitons	soliton	NOUN
ejde-1401	272	10	on	on	ADP
ejde-1401	272	11	riemannian	riemannian	ADJ
ejde-1401	272	12	manifolds	manifold	NOUN
ejde-1401	272	13	admitting	admit	VERB
ejde-1401	272	14	certain	certain	ADJ
ejde-1401	272	15	vector	vector	NOUN
ejde-1401	272	16	field	field	NOUN
ejde-1401	272	17	,	,	PUNCT
ejde-1401	272	18	ricerche	ricerche	PROPN
ejde-1401	272	19	mat	mat	PROPN
ejde-1401	272	20	.	.	PROPN
ejde-1401	272	21	,	,	PUNCT
ejde-1401	272	22	73	73	NUM
ejde-1401	272	23	(	(	PUNCT
ejde-1401	272	24	2024	2024	NUM
ejde-1401	272	25	)	)	PUNCT
ejde-1401	272	26	,	,	PUNCT
ejde-1401	272	27	531–546	531–546	NUM
ejde-1401	272	28	.	.	PUNCT
ejde-1401	273	1	[	[	X
ejde-1401	273	2	17	17	NUM
ejde-1401	273	3	]	]	X
ejde-1401	273	4	d.	d.	PROPN
ejde-1401	273	5	m.	m.	PROPN
ejde-1401	273	6	naik	naik	PROPN
ejde-1401	273	7	,	,	PUNCT
ejde-1401	273	8	g.	g.	PROPN
ejde-1401	273	9	f.	f.	PROPN
ejde-1401	273	10	ramandi	ramandi	PROPN
ejde-1401	273	11	,	,	PUNCT
ejde-1401	273	12	h.	h.	PROPN
ejde-1401	273	13	a.	a.	PROPN
ejde-1401	273	14	kumara	kumara	PROPN
ejde-1401	273	15	,	,	PUNCT
ejde-1401	273	16	v.	v.	ADP
ejde-1401	273	17	venkatesha	venkatesha	PROPN
ejde-1401	273	18	;	;	PUNCT
ejde-1401	273	19	yamabe	yamabe	ADJ
ejde-1401	273	20	solitons	soliton	NOUN
ejde-1401	273	21	and	and	CCONJ
ejde-1401	273	22	τ	τ	PROPN
ejde-1401	273	23	-quasi	-quasi	PROPN
ejde-1401	273	24	yamabe	yamabe	ADJ
ejde-1401	273	25	gradient	gradient	ADJ
ejde-1401	273	26	solitons	soliton	NOUN
ejde-1401	273	27	on	on	ADP
ejde-1401	273	28	riemannian	riemannian	ADJ
ejde-1401	273	29	manifolds	manifold	NOUN
ejde-1401	273	30	admitting	admit	VERB
ejde-1401	273	31	concurrent	concurrent	ADJ
ejde-1401	273	32	-	-	PUNCT
ejde-1401	273	33	recurrent	recurrent	NOUN
ejde-1401	273	34	vector	vector	NOUN
ejde-1401	273	35	fields	field	NOUN
ejde-1401	273	36	,	,	PUNCT
ejde-1401	273	37	math	math	NOUN
ejde-1401	273	38	.	.	PUNCT
ejde-1401	274	1	slovaca	slovaca	PROPN
ejde-1401	274	2	,	,	PUNCT
ejde-1401	274	3	73	73	NUM
ejde-1401	274	4	(	(	PUNCT
ejde-1401	274	5	2023	2023	NUM
ejde-1401	274	6	)	)	PUNCT
ejde-1401	274	7	,	,	PUNCT
ejde-1401	274	8	501–510	501–510	NUM
ejde-1401	274	9	.	.	PUNCT
ejde-1401	275	1	[	[	X
ejde-1401	275	2	18	18	NUM
ejde-1401	275	3	]	]	X
ejde-1401	275	4	h.	h.	PROPN
ejde-1401	275	5	omori	omori	PROPN
ejde-1401	275	6	;	;	PUNCT
ejde-1401	275	7	isometric	isometric	ADJ
ejde-1401	275	8	immersions	immersion	NOUN
ejde-1401	275	9	of	of	ADP
ejde-1401	275	10	riemannian	riemannian	ADJ
ejde-1401	275	11	manifolds	manifold	NOUN
ejde-1401	275	12	,	,	PUNCT
ejde-1401	275	13	j.	j.	PROPN
ejde-1401	275	14	math	math	PROPN
ejde-1401	275	15	.	.	PUNCT
ejde-1401	275	16	soc	soc	PROPN
ejde-1401	275	17	.	.	PUNCT
ejde-1401	276	1	japan	japan	PROPN
ejde-1401	276	2	,	,	PUNCT
ejde-1401	276	3	19	19	NUM
ejde-1401	276	4	(	(	PUNCT
ejde-1401	276	5	1967	1967	NUM
ejde-1401	276	6	)	)	PUNCT
ejde-1401	276	7	,	,	PUNCT
ejde-1401	276	8	205–214	205–214	NUM
ejde-1401	276	9	.	.	PUNCT
ejde-1401	277	1	[	[	X
ejde-1401	277	2	19	19	NUM
ejde-1401	277	3	]	]	X
ejde-1401	277	4	s.	s.	PROPN
ejde-1401	277	5	pigola	pigola	PROPN
ejde-1401	277	6	,	,	PUNCT
ejde-1401	277	7	m.	m.	NOUN
ejde-1401	277	8	rigoli	rigoli	NOUN
ejde-1401	277	9	,	,	PUNCT
ejde-1401	277	10	a.	a.	NOUN
ejde-1401	277	11	g.	g.	PROPN
ejde-1401	277	12	setti	setti	PROPN
ejde-1401	277	13	;	;	PUNCT
ejde-1401	277	14	a	a	DET
ejde-1401	277	15	remark	remark	NOUN
ejde-1401	277	16	on	on	ADP
ejde-1401	277	17	the	the	DET
ejde-1401	277	18	maximum	maximum	ADJ
ejde-1401	277	19	principle	principle	NOUN
ejde-1401	277	20	and	and	CCONJ
ejde-1401	277	21	stochastic	stochastic	ADJ
ejde-1401	277	22	completeness	completeness	NOUN
ejde-1401	277	23	,	,	PUNCT
ejde-1401	277	24	proc	proc	NOUN
ejde-1401	277	25	.	.	PUNCT
ejde-1401	278	1	amer	amer	PROPN
ejde-1401	278	2	.	.	PUNCT
ejde-1401	278	3	math	math	PROPN
ejde-1401	278	4	.	.	PUNCT
ejde-1401	279	1	soc	soc	PROPN
ejde-1401	279	2	.	.	PUNCT
ejde-1401	279	3	,	,	PUNCT
ejde-1401	279	4	131	131	NUM
ejde-1401	279	5	(	(	PUNCT
ejde-1401	279	6	2002	2002	NUM
ejde-1401	279	7	)	)	PUNCT
ejde-1401	279	8	,	,	PUNCT
ejde-1401	279	9	1283–1288	1283–1288	NUM
ejde-1401	279	10	.	.	PUNCT
ejde-1401	280	1	[	[	X
ejde-1401	280	2	20	20	NUM
ejde-1401	280	3	]	]	PUNCT
ejde-1401	280	4	s.	s.	PROPN
ejde-1401	280	5	pigola	pigola	PROPN
ejde-1401	280	6	,	,	PUNCT
ejde-1401	280	7	m.	m.	NOUN
ejde-1401	280	8	rigoli	rigoli	NOUN
ejde-1401	280	9	,	,	PUNCT
ejde-1401	280	10	a.g	a.g	PROPN
ejde-1401	280	11	.	.	PROPN
ejde-1401	280	12	setti	setti	PROPN
ejde-1401	280	13	;	;	PUNCT
ejde-1401	280	14	maximum	maximum	ADJ
ejde-1401	280	15	principles	principle	NOUN
ejde-1401	280	16	on	on	ADP
ejde-1401	280	17	riemannian	riemannian	ADJ
ejde-1401	280	18	manifolds	manifold	NOUN
ejde-1401	280	19	and	and	CCONJ
ejde-1401	280	20	applications	application	NOUN
ejde-1401	280	21	,	,	PUNCT
ejde-1401	280	22	mem	mem	PROPN
ejde-1401	280	23	.	.	PUNCT
ejde-1401	280	24	amer	amer	PROPN
ejde-1401	280	25	.	.	PUNCT
ejde-1401	280	26	math	math	PROPN
ejde-1401	280	27	.	.	PUNCT
ejde-1401	281	1	soc	soc	PROPN
ejde-1401	281	2	.	.	PROPN
ejde-1401	281	3	,	,	PUNCT
ejde-1401	281	4	174	174	NUM
ejde-1401	281	5	,	,	PUNCT
ejde-1401	281	6	no	no	INTJ
ejde-1401	281	7	.	.	NOUN
ejde-1401	281	8	822	822	NUM
ejde-1401	281	9	,	,	PUNCT
ejde-1401	281	10	(	(	PUNCT
ejde-1401	281	11	2005	2005	NUM
ejde-1401	281	12	)	)	PUNCT
ejde-1401	281	13	,	,	PUNCT
ejde-1401	281	14	x+99	x+99	PROPN
ejde-1401	281	15	pp	pp	PROPN
ejde-1401	281	16	.	.	PUNCT
ejde-1401	282	1	[	[	X
ejde-1401	282	2	21	21	NUM
ejde-1401	282	3	]	]	X
ejde-1401	282	4	s.	s.	PROPN
ejde-1401	282	5	pigola	pigola	PROPN
ejde-1401	282	6	,	,	PUNCT
ejde-1401	282	7	m.	m.	NOUN
ejde-1401	282	8	rigoli	rigoli	NOUN
ejde-1401	282	9	,	,	PUNCT
ejde-1401	282	10	a.g	a.g	PROPN
ejde-1401	282	11	.	.	PROPN
ejde-1401	282	12	setti	setti	PROPN
ejde-1401	282	13	;	;	PUNCT
ejde-1401	282	14	vanishing	vanish	VERB
ejde-1401	282	15	theorems	theorem	NOUN
ejde-1401	282	16	on	on	ADP
ejde-1401	282	17	riemannian	riemannian	ADJ
ejde-1401	282	18	manifolds	manifold	NOUN
ejde-1401	282	19	and	and	CCONJ
ejde-1401	282	20	geometric	geometric	ADJ
ejde-1401	282	21	applications	application	NOUN
ejde-1401	282	22	,	,	PUNCT
ejde-1401	282	23	j.	j.	PROPN
ejde-1401	282	24	funct	funct	PROPN
ejde-1401	282	25	.	.	PUNCT
ejde-1401	283	1	anal	anal	PROPN
ejde-1401	283	2	.	.	PROPN
ejde-1401	283	3	,	,	PUNCT
ejde-1401	283	4	229	229	NUM
ejde-1401	283	5	(	(	PUNCT
ejde-1401	283	6	2005	2005	NUM
ejde-1401	283	7	)	)	PUNCT
ejde-1401	283	8	,	,	PUNCT
ejde-1401	283	9	424–461	424–461	NUM
ejde-1401	283	10	.	.	PUNCT
ejde-1401	284	1	[	[	X
ejde-1401	284	2	22	22	NUM
ejde-1401	284	3	]	]	X
ejde-1401	284	4	r.	r.	PROPN
ejde-1401	284	5	poddar	poddar	PROPN
ejde-1401	284	6	,	,	PUNCT
ejde-1401	284	7	r.	r.	PROPN
ejde-1401	284	8	sharma	sharma	PROPN
ejde-1401	284	9	,	,	PUNCT
ejde-1401	284	10	b.	b.	PROPN
ejde-1401	284	11	subramanian	subramanian	PROPN
ejde-1401	284	12	;	;	PUNCT
ejde-1401	284	13	notes	note	NOUN
ejde-1401	284	14	on	on	ADP
ejde-1401	284	15	m	m	NOUN
ejde-1401	284	16	-	-	PUNCT
ejde-1401	284	17	quasi	quasi	ADJ
ejde-1401	284	18	yamabe	yamabe	PROPN
ejde-1401	284	19	gradient	gradient	PROPN
ejde-1401	284	20	solitons	soliton	NOUN
ejde-1401	284	21	,	,	PUNCT
ejde-1401	284	22	proc	proc	NOUN
ejde-1401	284	23	.	.	PUNCT
ejde-1401	284	24	math	math	NOUN
ejde-1401	284	25	.	.	PUNCT
ejde-1401	285	1	sci	sci	PROPN
ejde-1401	285	2	.	.	PROPN
ejde-1401	285	3	,	,	PUNCT
ejde-1401	285	4	134	134	NUM
ejde-1401	285	5	,	,	PUNCT
ejde-1401	285	6	2	2	NUM
ejde-1401	285	7	(	(	PUNCT
ejde-1401	285	8	2024	2024	NUM
ejde-1401	285	9	)	)	PUNCT
ejde-1401	285	10	.	.	PUNCT
ejde-1401	286	1	[	[	X
ejde-1401	286	2	23	23	NUM
ejde-1401	286	3	]	]	X
ejde-1401	286	4	r.	r.	PROPN
ejde-1401	286	5	schoen	schoen	PROPN
ejde-1401	286	6	;	;	PUNCT
ejde-1401	286	7	conformal	conformal	ADJ
ejde-1401	286	8	deformation	deformation	NOUN
ejde-1401	286	9	of	of	ADP
ejde-1401	286	10	a	a	DET
ejde-1401	286	11	riemannian	riemannian	ADJ
ejde-1401	286	12	metric	metric	NOUN
ejde-1401	286	13	to	to	PART
ejde-1401	286	14	constant	constant	ADJ
ejde-1401	286	15	scalar	scalar	ADJ
ejde-1401	286	16	curvature	curvature	NOUN
ejde-1401	286	17	,	,	PUNCT
ejde-1401	286	18	j.	j.	PROPN
ejde-1401	286	19	diff	diff	PROPN
ejde-1401	286	20	.	.	PUNCT
ejde-1401	287	1	geom	geom	PROPN
ejde-1401	287	2	.	.	PROPN
ejde-1401	287	3	,	,	PUNCT
ejde-1401	287	4	20	20	NUM
ejde-1401	287	5	(	(	PUNCT
ejde-1401	287	6	1984	1984	NUM
ejde-1401	287	7	)	)	PUNCT
ejde-1401	287	8	,	,	PUNCT
ejde-1401	287	9	479–495	479–495	NUM
ejde-1401	287	10	.	.	PUNCT
ejde-1401	288	1	[	[	X
ejde-1401	288	2	24	24	NUM
ejde-1401	288	3	]	]	X
ejde-1401	288	4	d.	d.	PROPN
ejde-1401	288	5	stroock	stroock	PROPN
ejde-1401	288	6	;	;	PUNCT
ejde-1401	288	7	an	an	DET
ejde-1401	288	8	introduction	introduction	NOUN
ejde-1401	288	9	to	to	ADP
ejde-1401	288	10	the	the	DET
ejde-1401	288	11	analysis	analysis	NOUN
ejde-1401	288	12	of	of	ADP
ejde-1401	288	13	paths	path	NOUN
ejde-1401	288	14	on	on	ADP
ejde-1401	288	15	a	a	DET
ejde-1401	288	16	riemannian	riemannian	ADJ
ejde-1401	288	17	manifold	manifold	NOUN
ejde-1401	288	18	,	,	PUNCT
ejde-1401	288	19	math	math	NOUN
ejde-1401	288	20	.	.	PUNCT
ejde-1401	289	1	surveys	survey	NOUN
ejde-1401	289	2	and	and	CCONJ
ejde-1401	289	3	monographs	monograph	NOUN
ejde-1401	289	4	,	,	PUNCT
ejde-1401	289	5	volume	volume	NOUN
ejde-1401	289	6	4	4	NUM
ejde-1401	289	7	,	,	PUNCT
ejde-1401	289	8	american	american	ADJ
ejde-1401	289	9	math	math	NOUN
ejde-1401	289	10	.	.	PUNCT
ejde-1401	290	1	soc	soc	PROPN
ejde-1401	290	2	.	.	PROPN
ejde-1401	290	3	,	,	PUNCT
ejde-1401	290	4	2000	2000	NUM
ejde-1401	290	5	.	.	PUNCT
ejde-1401	291	1	10	10	NUM
ejde-1401	291	2	g.	g.	PROPN
ejde-1401	291	3	molica	molica	PROPN
ejde-1401	291	4	bisci	bisci	PROPN
ejde-1401	291	5	,	,	PUNCT
ejde-1401	291	6	h.	h.	PROPN
ejde-1401	291	7	f.	f.	PROPN
ejde-1401	291	8	de	de	PROPN
ejde-1401	291	9	lima	lima	PROPN
ejde-1401	291	10	,	,	PUNCT
ejde-1401	291	11	a.	a.	PROPN
ejde-1401	291	12	v.	v.	PROPN
ejde-1401	291	13	f.	f.	PROPN
ejde-1401	291	14	leite	leite	PROPN
ejde-1401	291	15	,	,	PUNCT
ejde-1401	291	16	m.	m.	NOUN
ejde-1401	291	17	a.	a.	PROPN
ejde-1401	291	18	l.	l.	PROPN
ejde-1401	291	19	velásquez	velásquez	PROPN
ejde-1401	291	20	ejde-2025/62	ejde-2025/62	PROPN
ejde-1401	292	1	[	[	X
ejde-1401	292	2	25	25	NUM
ejde-1401	292	3	]	]	X
ejde-1401	292	4	n.	n.	NOUN
ejde-1401	292	5	trudinger	trudinger	NOUN
ejde-1401	292	6	;	;	PUNCT
ejde-1401	292	7	remarks	remark	NOUN
ejde-1401	292	8	concerning	concern	VERB
ejde-1401	292	9	the	the	DET
ejde-1401	292	10	conformai	conformai	ADJ
ejde-1401	292	11	deformation	deformation	NOUN
ejde-1401	292	12	of	of	ADP
ejde-1401	292	13	riemannian	riemannian	ADJ
ejde-1401	292	14	structures	structure	NOUN
ejde-1401	292	15	on	on	ADP
ejde-1401	292	16	compact	compact	ADJ
ejde-1401	292	17	manifolds	manifold	NOUN
ejde-1401	292	18	,	,	PUNCT
ejde-1401	292	19	ann	ann	PROPN
ejde-1401	292	20	.	.	PROPN
ejde-1401	292	21	scuola	scuola	PROPN
ejde-1401	292	22	norm	norm	NOUN
ejde-1401	292	23	.	.	PUNCT
ejde-1401	293	1	sup	sup	NOUN
ejde-1401	293	2	.	.	PUNCT
ejde-1401	294	1	pisa	pisa	PROPN
ejde-1401	294	2	,	,	PUNCT
ejde-1401	294	3	22	22	NUM
ejde-1401	294	4	(	(	PUNCT
ejde-1401	294	5	1968	1968	NUM
ejde-1401	294	6	)	)	PUNCT
ejde-1401	294	7	,	,	PUNCT
ejde-1401	294	8	265–274	265–274	NUM
ejde-1401	294	9	.	.	PUNCT
ejde-1401	295	1	[	[	X
ejde-1401	295	2	26	26	NUM
ejde-1401	295	3	]	]	X
ejde-1401	295	4	l.	l.	PROPN
ejde-1401	295	5	f.	f.	PROPN
ejde-1401	295	6	wang	wang	PROPN
ejde-1401	295	7	;	;	PUNCT
ejde-1401	295	8	on	on	ADP
ejde-1401	295	9	noncompact	noncompact	NOUN
ejde-1401	295	10	quasi	quasi	ADJ
ejde-1401	295	11	yamabe	yamabe	PROPN
ejde-1401	295	12	gradient	gradient	PROPN
ejde-1401	295	13	solitons	soliton	NOUN
ejde-1401	295	14	,	,	PUNCT
ejde-1401	295	15	diff	diff	PROPN
ejde-1401	295	16	.	.	PUNCT
ejde-1401	296	1	geom	geom	PROPN
ejde-1401	296	2	.	.	PUNCT
ejde-1401	297	1	appl	appl	PROPN
ejde-1401	297	2	.	.	PROPN
ejde-1401	297	3	,	,	PUNCT
ejde-1401	297	4	31	31	NUM
ejde-1401	297	5	(	(	PUNCT
ejde-1401	297	6	2013	2013	NUM
ejde-1401	297	7	)	)	PUNCT
ejde-1401	297	8	,	,	PUNCT
ejde-1401	297	9	337–348	337–348	NUM
ejde-1401	297	10	.	.	PUNCT
ejde-1401	298	1	[	[	X
ejde-1401	298	2	27	27	NUM
ejde-1401	298	3	]	]	X
ejde-1401	298	4	h.	h.	PROPN
ejde-1401	298	5	yamabe	yamabe	PROPN
ejde-1401	298	6	;	;	PUNCT
ejde-1401	298	7	on	on	ADP
ejde-1401	298	8	a	a	DET
ejde-1401	298	9	deformation	deformation	NOUN
ejde-1401	298	10	of	of	ADP
ejde-1401	298	11	riemannian	riemannian	ADJ
ejde-1401	298	12	structures	structure	NOUN
ejde-1401	298	13	on	on	ADP
ejde-1401	298	14	compact	compact	ADJ
ejde-1401	298	15	manifolds	manifold	NOUN
ejde-1401	298	16	,	,	PUNCT
ejde-1401	298	17	osaka	osaka	PROPN
ejde-1401	298	18	math	math	PROPN
ejde-1401	298	19	.	.	PUNCT
ejde-1401	299	1	j.	j.	PROPN
ejde-1401	299	2	,	,	PUNCT
ejde-1401	299	3	12	12	NUM
ejde-1401	299	4	(	(	PUNCT
ejde-1401	299	5	1960	1960	NUM
ejde-1401	299	6	)	)	PUNCT
ejde-1401	299	7	,	,	PUNCT
ejde-1401	299	8	21–37	21–37	NUM
ejde-1401	299	9	.	.	PUNCT
ejde-1401	300	1	[	[	X
ejde-1401	300	2	28	28	NUM
ejde-1401	300	3	]	]	X
ejde-1401	300	4	s.t	s.t	PROPN
ejde-1401	300	5	.	.	PUNCT
ejde-1401	301	1	yau	yau	PROPN
ejde-1401	301	2	;	;	PUNCT
ejde-1401	301	3	harmonic	harmonic	ADJ
ejde-1401	301	4	functions	function	NOUN
ejde-1401	301	5	on	on	ADP
ejde-1401	301	6	complete	complete	ADJ
ejde-1401	301	7	riemannian	riemannian	ADJ
ejde-1401	301	8	manifolds	manifold	NOUN
ejde-1401	301	9	,	,	PUNCT
ejde-1401	301	10	comm	comm	NOUN
ejde-1401	301	11	.	.	PUNCT
ejde-1401	302	1	pure	pure	ADJ
ejde-1401	302	2	appl	appl	PROPN
ejde-1401	302	3	.	.	PUNCT
ejde-1401	302	4	math	math	PROPN
ejde-1401	302	5	.	.	PUNCT
ejde-1401	303	1	,	,	PUNCT
ejde-1401	303	2	28	28	NUM
ejde-1401	303	3	(	(	PUNCT
ejde-1401	303	4	1975	1975	NUM
ejde-1401	303	5	)	)	PUNCT
ejde-1401	303	6	,	,	PUNCT
ejde-1401	303	7	201–228	201–228	NUM
ejde-1401	303	8	.	.	PUNCT
ejde-1401	304	1	[	[	X
ejde-1401	304	2	29	29	NUM
ejde-1401	304	3	]	]	X
ejde-1401	304	4	s.t	s.t	PROPN
ejde-1401	304	5	.	.	PROPN
ejde-1401	304	6	yau	yau	PROPN
ejde-1401	304	7	;	;	PUNCT
ejde-1401	304	8	some	some	DET
ejde-1401	304	9	function	function	NOUN
ejde-1401	304	10	-	-	PUNCT
ejde-1401	304	11	theoretic	theoretic	NOUN
ejde-1401	304	12	properties	property	NOUN
ejde-1401	304	13	of	of	ADP
ejde-1401	304	14	complete	complete	ADJ
ejde-1401	304	15	riemannian	riemannian	ADJ
ejde-1401	304	16	manifolds	manifold	NOUN
ejde-1401	304	17	and	and	CCONJ
ejde-1401	304	18	their	their	PRON
ejde-1401	304	19	applications	application	NOUN
ejde-1401	304	20	to	to	ADP
ejde-1401	304	21	geometry	geometry	NOUN
ejde-1401	304	22	,	,	PUNCT
ejde-1401	304	23	indiana	indiana	PROPN
ejde-1401	304	24	univ	univ	PROPN
ejde-1401	304	25	.	.	PUNCT
ejde-1401	304	26	math	math	PROPN
ejde-1401	304	27	.	.	PUNCT
ejde-1401	305	1	j.	j.	PROPN
ejde-1401	305	2	,	,	PUNCT
ejde-1401	305	3	25	25	NUM
ejde-1401	305	4	(	(	PUNCT
ejde-1401	305	5	1976	1976	NUM
ejde-1401	305	6	)	)	PUNCT
ejde-1401	305	7	,	,	PUNCT
ejde-1401	305	8	659–670	659–670	NUM
ejde-1401	305	9	.	.	PUNCT
ejde-1401	306	1	giovanni	giovanni	PROPN
ejde-1401	306	2	molica	molica	PROPN
ejde-1401	306	3	bisci	bisci	PROPN
ejde-1401	306	4	department	department	PROPN
ejde-1401	306	5	of	of	ADP
ejde-1401	306	6	human	human	PROPN
ejde-1401	306	7	sciences	science	NOUN
ejde-1401	306	8	and	and	CCONJ
ejde-1401	306	9	quality	quality	NOUN
ejde-1401	306	10	of	of	ADP
ejde-1401	306	11	life	life	NOUN
ejde-1401	306	12	promotion	promotion	NOUN
ejde-1401	306	13	,	,	PUNCT
ejde-1401	306	14	san	san	PROPN
ejde-1401	306	15	raffaele	raffaele	PROPN
ejde-1401	306	16	university	university	PROPN
ejde-1401	306	17	of	of	ADP
ejde-1401	306	18	rome	rome	PROPN
ejde-1401	306	19	,	,	PUNCT
ejde-1401	306	20	rome	rome	PROPN
ejde-1401	306	21	,	,	PUNCT
ejde-1401	306	22	italy	italy	PROPN
ejde-1401	306	23	email	email	NOUN
ejde-1401	306	24	address	address	NOUN
ejde-1401	306	25	:	:	PUNCT
ejde-1401	306	26	giovanni.molicabisci@uniroma5.it	giovanni.molicabisci@uniroma5.it	X
ejde-1401	306	27	henrique	henrique	PROPN
ejde-1401	306	28	f.	f.	PROPN
ejde-1401	306	29	de	de	PROPN
ejde-1401	306	30	lima	lima	PROPN
ejde-1401	306	31	departamento	departamento	PROPN
ejde-1401	306	32	de	de	PROPN
ejde-1401	306	33	matemática	matemática	PROPN
ejde-1401	306	34	,	,	PUNCT
ejde-1401	306	35	universidade	universidade	PROPN
ejde-1401	306	36	federal	federal	PROPN
ejde-1401	306	37	de	de	PROPN
ejde-1401	306	38	campina	campina	PROPN
ejde-1401	306	39	grande	grande	PROPN
ejde-1401	306	40	,	,	PUNCT
ejde-1401	306	41	58.429	58.429	PROPN
ejde-1401	306	42	-	-	SYM
ejde-1401	306	43	970	970	NUM
ejde-1401	306	44	campina	campina	PROPN
ejde-1401	306	45	grande	grande	PROPN
ejde-1401	306	46	,	,	PUNCT
ejde-1401	306	47	paráıba	paráıba	ADJ
ejde-1401	306	48	,	,	PUNCT
ejde-1401	306	49	brazil	brazil	PROPN
ejde-1401	306	50	email	email	NOUN
ejde-1401	306	51	address	address	NOUN
ejde-1401	306	52	:	:	PUNCT
ejde-1401	306	53	henriquedelima74@gmail.com	henriquedelima74@gmail.com	X
ejde-1401	306	54	ary	ary	PROPN
ejde-1401	306	55	v.	v.	PROPN
ejde-1401	306	56	f.	f.	PROPN
ejde-1401	306	57	leite	leite	PROPN
ejde-1401	306	58	departamento	departamento	PROPN
ejde-1401	306	59	de	de	PROPN
ejde-1401	306	60	matemática	matemática	PROPN
ejde-1401	306	61	,	,	PUNCT
ejde-1401	306	62	universidade	universidade	PROPN
ejde-1401	306	63	federal	federal	PROPN
ejde-1401	306	64	de	de	PROPN
ejde-1401	306	65	campina	campina	PROPN
ejde-1401	306	66	grande	grande	PROPN
ejde-1401	306	67	,	,	PUNCT
ejde-1401	306	68	58.429	58.429	PROPN
ejde-1401	306	69	-	-	SYM
ejde-1401	306	70	970	970	NUM
ejde-1401	306	71	campina	campina	PROPN
ejde-1401	306	72	grande	grande	PROPN
ejde-1401	306	73	,	,	PUNCT
ejde-1401	306	74	paráıba	paráıba	ADJ
ejde-1401	306	75	,	,	PUNCT
ejde-1401	306	76	brazil	brazil	PROPN
ejde-1401	306	77	email	email	NOUN
ejde-1401	306	78	address	address	NOUN
ejde-1401	306	79	:	:	PUNCT
ejde-1401	307	1	ary.v.l.f@gmail.com	ary.v.l.f@gmail.com	PROPN
ejde-1401	307	2	marco	marco	PROPN
ejde-1401	307	3	a.	a.	PROPN
ejde-1401	307	4	l.	l.	PROPN
ejde-1401	307	5	velásquez	velásquez	PROPN
ejde-1401	307	6	departamento	departamento	PROPN
ejde-1401	307	7	de	de	PROPN
ejde-1401	307	8	matemática	matemática	PROPN
ejde-1401	307	9	,	,	PUNCT
ejde-1401	307	10	universidade	universidade	PROPN
ejde-1401	307	11	federal	federal	PROPN
ejde-1401	307	12	de	de	PROPN
ejde-1401	307	13	campina	campina	PROPN
ejde-1401	307	14	grande	grande	PROPN
ejde-1401	307	15	,	,	PUNCT
ejde-1401	307	16	58.429	58.429	PROPN
ejde-1401	307	17	-	-	SYM
ejde-1401	307	18	970	970	NUM
ejde-1401	307	19	campina	campina	PROPN
ejde-1401	307	20	grande	grande	PROPN
ejde-1401	307	21	,	,	PUNCT
ejde-1401	307	22	paráıba	paráıba	ADJ
ejde-1401	307	23	,	,	PUNCT
ejde-1401	307	24	brazil	brazil	PROPN
ejde-1401	307	25	email	email	NOUN
ejde-1401	307	26	address	address	NOUN
ejde-1401	307	27	:	:	PUNCT
ejde-1401	307	28	marcolazarovelasquez@gmail.com	marcolazarovelasquez@gmail.com	X
ejde-1401	308	1	1	1	X
ejde-1401	308	2	.	.	PUNCT
ejde-1401	308	3	introduction	introduction	NOUN
ejde-1401	308	4	2	2	NUM
ejde-1401	308	5	.	.	NOUN
ejde-1401	308	6	suitable	suitable	ADJ
ejde-1401	308	7	bochner	bochner	NOUN
ejde-1401	308	8	type	type	NOUN
ejde-1401	308	9	formula	formula	NOUN
ejde-1401	308	10	3	3	NUM
ejde-1401	308	11	.	.	PUNCT
ejde-1401	308	12	main	main	ADJ
ejde-1401	308	13	results	result	NOUN
ejde-1401	308	14	3.1	3.1	NUM
ejde-1401	308	15	.	.	PUNCT
ejde-1401	309	1	via	via	ADP
ejde-1401	309	2	integrability	integrability	NOUN
ejde-1401	309	3	conditions	condition	NOUN
ejde-1401	309	4	3.2	3.2	NUM
ejde-1401	309	5	.	.	PUNCT
ejde-1401	310	1	via	via	ADP
ejde-1401	310	2	volume	volume	NOUN
ejde-1401	310	3	growth	growth	NOUN
ejde-1401	310	4	3.3	3.3	NUM
ejde-1401	310	5	.	.	PUNCT
ejde-1401	311	1	via	via	ADP
ejde-1401	311	2	stochastic	stochastic	ADJ
ejde-1401	311	3	completeness	completeness	NOUN
ejde-1401	311	4	3.4	3.4	NUM
ejde-1401	311	5	.	.	PUNCT
ejde-1401	312	1	via	via	ADP
ejde-1401	312	2	convergence	convergence	NOUN
ejde-1401	312	3	at	at	ADP
ejde-1401	312	4	infinity	infinity	NOUN
ejde-1401	312	5	acknowledgements	acknowledgement	NOUN
ejde-1401	312	6	references	reference	NOUN