HARMONIC MAPS FROM NONCOMPACT RIEMANNIAN-MANIFOLDS WITH NONNEGATIVE RICCI CURVATURE OUTSIDE A COMPACT SET

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 S-2(M) > 0 and Ricci curvature Ric (M) greater than or equal to 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).