Nagoya Mathematical Journal

Uniformly perfect sets and distortion of holomorphic functions

Jian-Hua Zheng

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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 $\Delta$ 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

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

First available in Project Euclid: 27 April 2005

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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


Zheng, Jian-Hua. Uniformly perfect sets and distortion of holomorphic functions. Nagoya Math. J. 164 (2001), 17--33.

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