1996/09/21 by Deane Yang, Yang, Deane
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #dg-ga #math.DG
paper · pdf · doi:10.48550/arxiv.dg-ga/9609008
Major revision of earlier submission, 16 pages, AMSLaTeX
arxiv created 1997/03/23 · arxiv updated 2009/11/30
Using a flow first introduced by J.P. Anderson, we obtain some existence theorems for harmonic maps from a noncompact complete Riemannian manifold into a complete Riemannian manifold. In particular, we prove as a corollary a recent result of Hardt and Wolf stating that any quasisymmetric map of the sphere that is sufficiently close to the identity can be extended to a quasiconformal harmonic diffeomorphism of the hyperbolic ball. This version contains a much simpler proof than the first version.