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The existence of bounded harmonic functions on C-H manifolds. (English) Zbl 0885.53036
Let $$M$$ be a simply connected complete Riemannian manifold with sectional curvatures $$-b^2\leq K_M (\sigma) \leq- A/r^2$$, where $$r$$ is the distance of the footpoint of $$\sigma$$ to a fixed origin of $$M$$ and where $$A>4$$. The authors show that under these assumptions the Dirichlet problem at infinity can be solved.
Reviewer: W.Ballmann (Bonn)

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