  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.
