id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejpam-460	Zhichun, Xie; Xinzhong, Huang	On the Solutions for Grotzsch Annulus Extremal problem	2009	12	.pdf	application/pdf	2958	165	85	If f (z) satisfies |S|hyp | f (S)|hyp = (R2 2 − R2 1 )(1− R2K 2 )(1− R2K 1 ) (R2K 2 − R2K 1 )(1− R2 2)(1− R2 1) , REFERENCES 543 and K[ f ] = K, then f (z) is an extremal quasiconformal mapping from S onto S′, and f (z) = rK ei(θ+α), z = reiθ , where α is a constant. ACKNOWLEDGEMENTS The authors would like to thank the referee very much for his many valuable suggestions. Suppose that f (z) is a quasiconformal mapping in Ω, let D f (z) = | fz|+| fz̄	cache/ejpam-460.pdf	txt/ejpam-460.txt