## The Dirichlet problem at infinity for a negatively curved manifold.(English)Zbl 0541.53037

Let M be a simply connected Riemannian manifold with sectional curvature bounded between two negative constants. The author uses probability theory to prove that each continuous function on the sphere at infinity $$\partial \bar M$$ has a continuous harmonic extension to $$M\cup \partial \bar M$$. As a consequence it follows that there are many non-constant bounded harmonic functions on M. This result was proved independently by M. T. Anderson by a different method [see the preceding review].
Reviewer: G.Thorbergsson

### MSC:

 53C20 Global Riemannian geometry, including pinching 31C05 Harmonic, subharmonic, superharmonic functions on other spaces

### Citations:

Zbl 0541.53035; Zbl 0541.53036
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