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Uniformly perfect sets and distortion of holomorphic functions

Published online by Cambridge University Press:  22 January 2016

Jian-Hua Zheng
Jian-Hua Zheng*
Affiliation:
Department of Mathematical Science, Tsing Hua University, Beijing, P. R. China, jzheng@math.tsinghua.edu.cn
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Abstract

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We investigate the uniform perfectness on a boundary point of a hyperbolic open set and distortion of a holomorphic function from the unit disk Δ into a hyperbolic domain with a uniformly perfect boundary point, especially of a universal covering map of such a domain from Δ, and we obtain similar results to celebrated Koebe’s Theorems on univalent functions.

Keywords

30C8030F45
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 164 , December 2001 , pp. 17 - 33
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2001

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