Deforming a map into a harmonic map

Details Deforming a map into a harmonic map Deforming a map into a harmonic map

1996-09-21

arxiv.org/abs/dg-ga/9609008v2

Mathematics

Differential Geometry

Major revision of earlier submission, 16 pages, AMSLaTeX

Scientific paper

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.

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