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
