Asymptotic behaviour of harmonic functions in negative curvature
type: Item
instance of: scholarly article
title: Asymptotic behaviour of harmonic functions in negative curvature
zbMATH Open document ID: 0840.60018
DOI: 10.1007/BF02566019
author: Frédéric Mouton
published in: Commentarii Mathematici Helvetici
publication date: 1996-04-18T00:00:00Z
full work available at URL: https://eudml.org/doc/140380
review text: Summary: Let \(M\) be a complete simply connected Riemannian manifold whose sectional curvatures are bounded between two negative constants. It is shown that, for a given harmonic function on \(M\), non-tangential properties of convergence, boundedness and finiteness of energy are equivalent for almost every point of the geometric boundary. This is a ``geometric'' analogue of Calderón-Stein theorem in the Euclidean half-space. The proof is using Brownian motion, like J. Brossard's one for the Euclidean case.
Mathematics Subject Classification ID: 60D05
Mathematics Subject Classification ID: 58E20
Mathematics Subject Classification ID: 53C20
zbMATH DE Number: 838582
zbMATH Keywords: non-tangential properties of convergence
zbMATH Keywords: Brownian motion
MaRDI profile type: Publication
OpenAlex ID: W2011989938
description: scientific article; zbMATH DE number 838582