Home > Proceedings > Adv. Stud. Pure Math. > Potential Theory in Matsue > Quasiconformal mappings and minimal Martin boundary of $p$-sheeted unlimited covering surfaces of the once punctered Riemann sphere $\hat{\mathbb{C}} \setminus \{0\}$ of Heins type
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VOL. 44 | 2006 Quasiconformal mappings and minimal Martin boundary of $p$-sheeted unlimited covering surfaces of the once punctered Riemann sphere $\hat{\mathbb{C}} \setminus \{0\}$ of Heins type
Hiroaki Masaoka

Editor(s) Hiroaki Aikawa, Takashi Kumagai, Yoshihiro Mizuta, Noriaki Suzuki

## Abstract

Let $R$ and $R'$ be $p$-sheeted unlimited covering surfaces of the once punctured Riemann sphere $\hat{\mathbb{C}} \setminus \{0\}$ of Heins type which are quasiconformal equivalent to each other. Then the cardinal numbers of minimal Martin boundaries of $R$ and $R'$ are same.

Let $R$ be a 2-sheeted unlimited covering surface of the once punctured Riemann sphere $\hat{\mathbb{C}} \setminus \{0\}$ of Heins type and $R'$ be an open Riemann surface. If $R$ and $R'$ are quasiconformal equivalent to each other and the set of branch points of $R$ satisfies a condition, then the cardinal numbers of minimal Martin boundaries of $R$ and $R'$ are same.

## Information

Published: 1 January 2006
First available in Project Euclid: 16 December 2018

zbMATH: 1123.31006
MathSciNet: MR2277835

Digital Object Identifier: 10.2969/aspm/04410211

Subjects:
Primary: 31C35
Secondary: 30F25

Keywords: covering surface , Martin boundary , quasiconformal mappings