Positive harmonic functions on abelian covers
type: Item
instance of: scholarly article
title: Positive harmonic functions on abelian covers
zbMATH Open document ID: 0685.31003
DOI: 10.1016/0022-1236(89)90073-6
author: Charles L. Epstein
published in: Journal of Functional Analysis
publication date: 1989-01-01T00:00:00Z
review text: The existence of positive harmonic functions and Green's functions on certain Abelian covers of non-compact, finite volume Riemann surfaces is shown. These results are obtained by studying the asymptotic distribution of the lattice in hyperbolic space generated by the fundamental group of the covering surface. They extend considerations by \textit{T.Lyons} and \textit{D. Sullivan} [J. Differ. Geom. 19, 299-323 (1984; Zbl 0554.58022)] on covers of compact Riemann surfaces using the theory of Brownian motion.
reviewed by: Wolfhard Hansen
Mathematics Subject Classification ID: 31C12
Mathematics Subject Classification ID: 31C05
Mathematics Subject Classification ID: 30F15
zbMATH DE Number: 4122309
zbMATH Keywords: Green's functions
zbMATH Keywords: hyperbolic space
zbMATH Keywords: positive harmonic functions
zbMATH Keywords: lattice
MaRDI profile type: Publication
full work available at URL: 0022-1236(89)90073-6
OpenAlex ID: W1992185251
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description: scientific article; zbMATH DE number 4122309