2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/148776Using 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.Major revision of earlier submission, 16 pages, AMSLaTeXDifferential Geometrytext