Joseph F. Grotowski, Manfred Kronz
Minimizing conformal energies in homotopy classes
We consider a minimizing sequence for the conformal energy in a given homotopy class of maps between two compact Riemannian manifolds M and N. In general this sequence will fail to be (strongly) convergent in the natural Sobolev class, but will have a weak limit which is not a priori in the original homotopy class. We prove a topological decomposition theorem: the homotopy class of the original map is given as the composition (in an appropriate sense) of the homotopy class of the weak limit with a finite number of free homotopy classes of maps from the sphere (with dimension that of the manifold M) into N. The method of proof shows that the weak limit is a minimizer in its homotopy class, and also shows that the homotopy classes of maps from the sphere occurring in the decomposition can be represented by minimizers in their respective classes.
Forum Mathematicum, Walter de Gruyter
Print ISSN: 0933-7741
Volume: 16, 09/2004
Pages: 841 - 864
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