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VOL. 44 | 2006 Hyperbolic Riemann surfaces without unbounded positive harmonic functions
Hiroaki Masaoka, Shigeo Segawa

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

Abstract

Let $R$ be an open Riemann surface with Green's functions. It is proved that there exist no unbounded positive harmonic functions on $R$ if and only if the minimal Martin boundary of $R$ consists of finitely many points with positive harmonic measure.

Information

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

zbMATH: 1121.31006
MathSciNet: MR2277836

Digital Object Identifier: 10.2969/aspm/04410227

Subjects:
Primary: 30F15 , 30F20 , 30F25 , 31C35

Keywords: harmonic measure , Hyperbolic Riemann surface , Martin boundary , positive harmonic function

Rights: Copyright © 2006 Mathematical Society of Japan

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