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On the Dirichlet problem at infinity for manifolds of nonpositive curvature. (English) Zbl 0661.53026

A complete simply connected Riemannian manifold \(M^ n\) with nonpositive sectional curvature is diffeomorphic to \({\mathbb{R}}^ n\) and admits a compactification by a sphere at infinity. One may ask whether for a given continuous function f at infinity there is a harmonic extension to M. This question is answered in the case that M admits a compact quotient.
Reviewer: W.Ballmann

MSC:

53C20 Global Riemannian geometry, including pinching
31C12 Potential theory on Riemannian manifolds and other spaces
60G50 Sums of independent random variables; random walks
58J65 Diffusion processes and stochastic analysis on manifolds
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