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Harmonic diffeomorphisms, minimizing harmonic maps and rotational symmetry. (English) Zbl 0686.58012
The aim of the paper is to investigate the harmonic diffeomorphisms of the unit ball B n of R n onto a Riemannian manifold. It is shown that for n=2 these diffeomorphisms are minimizing with respect to the energy functional over H 1 mappings with trace condition. For n3 it is given a sufficient condition for this property in terms of the metric tensor. The case of finitely many punctual singularities is also treated. Interesting applications, especially for n=3 and n=4, are indicated when the harmonic diffeomorphisms are SO(n)-equivariant in an appropriate sense. One answers some questions raised in papers of Gulliver, White, Jäger, Kaul, Baldes and Helein.
Reviewer: D.Motreanu

MSC:
58E20Harmonic maps between infinite-dimensional spaces
58E30Variational principles on infinite-dimensional spaces
53C42Immersions (differential geometry)