Nagoya Mathematical Journal

Uniformly perfect sets and distortion of holomorphic functions

Jian-Hua Zheng

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Abstract

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

Article information

Source
Nagoya Math. J., Volume 164 (2001), 17-33.

Dates
First available in Project Euclid: 27 April 2005

Permanent link to this document
https://projecteuclid.org/euclid.nmj/1114631652

Mathematical Reviews number (MathSciNet)
MR1869092

Zentralblatt MATH identifier
1033.30018

Subjects
Primary: 30F45: Conformal metrics (hyperbolic, Poincaré, distance functions)
Secondary: 30C80: Maximum principle; Schwarz's lemma, Lindelöf principle, analogues and generalizations; subordination

Citation

Zheng, Jian-Hua. Uniformly perfect sets and distortion of holomorphic functions. Nagoya Math. J. 164 (2001), 17--33. https://projecteuclid.org/euclid.nmj/1114631652


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