## 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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