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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
53/2005

Martin points on open manifolds of non-positive curvature

Jianguo Cao, Huijun Fan and François Ledrappier

Abstract

The Martin boundary of a Cartan-Hadamard manifold describes a fine geometric structure at infinity, which is a sub-space of positive harmonic functions. We describe conditions which ensure that some points of the sphere at infinity belong to the Martin boundary as well. In the case of the universal cover of a compact manifold with Ballmann rank one, we show that Martin points are generic and of full harmonic measure. The result of this paper provides a partial answer to an open problem of S. T. Yau.

Received:
May 30, 2005
Published:
Apr 12, 2010

Related publications

Preprint
2005 Repository Open Access
Jianguo Cao, Huijun Fan and Fran­cois Ledrappier

Martin points on open manifolds of non-positive curvature