Martin points on open manifolds of non-positive curvature

Cao, Jianguo; Fan, Huijun; Ledrappier, François

doi:10.1090/S0002-9947-07-04102-5

Martin points on open manifolds of non-positive curvature
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by Jianguo Cao, Huijun Fan and François Ledrappier PDF

Trans. Amer. Math. Soc. 359 (2007), 5697-5723 Request permission

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.

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