Locally minimizing harmonic maps from noncompact manifolds |
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Authors: | Wei-Yue Ding |
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Affiliation: | (1) Institute of Mathematics, Academia Sinica, 100080 Beijing, China |
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Abstract: | By introducing the “relative energy”, we develop a new method for finding harmonic maps from noncompact complete Riemannian manifolds with prescribed asympototic behaviour at infinity. This method is an extension of the well known direct method of energy-minimization for compact domains. As an application of our method, we show that the Dirichlet problem at infinity with Hölder continuous boundary data for harmonic maps from a Cartan-Hadarmard manifold with bounded negative curvature into a compact manifold, has a locally minimizing solution which is smooth near infinity. |
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