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Harmonic maps from noncompact Riemannian manifolds with non-negative Ricci curvature outside a compact set

Published online by Cambridge University Press:  14 November 2011

Youde Wang
Youde Wang
Affiliation:
Institute of Mathematics, Academia Sinica, Beijing, China
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Abstract

In this paper we prove the uniqueness and existence of harmonic maps of finite energy from a complete, noncompact Riemannian manifold (M, g) with Sobolev constant S2(M) > 0 and Ricci curvature Ric (M) ≧ 0 outside some compact subset, into a complete manifold of nonpositive curvature or a regular ball. In particular, we prove the uniqueness and existence of bounded harmonic functions on (M, g).

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 124 , Issue 6 , 1994 , pp. 1259 - 1275
Copyright
Copyright © Royal Society of Edinburgh 1994

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