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Bounded harmonic maps on a class of manifolds. (English) Zbl 0865.58015

The main result of the article is that if every bounded harmonic function defined near infinity of an end of a manifold \(M\) with respect to some compact set is asymptotically constant then every bounded harmonic map from \(M\) into a regular ball of another manifold is also asymptotically constant at the infinity of each end. There is no curvature assumption on \(M\). All manifolds are assumed to be connected.

MSC:

58E20 Harmonic maps, etc.
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