Harmonic maps with fixed singular sets |
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Authors: | Robert Hardt Libin Mou |
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Affiliation: | 1. Mathematics Department, Rice University, 77251, Houston, TX, USA 2. Department of Mathematics, University of Southern California, 90089, Los Angeles, CA, USA
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Abstract: | Suppose Ω is a smooth domain in Rm,N is a compact smooth Riemannian manifold, andZ is a fixed compact subset of Ω having finite (m − 3)-dimensional Minkowski content (e.g.,Z ism − 3 rectifiable). We consider various spaces of harmonic mapsu: Ω →N that have a singular setZ and controlled behavior nearZ. We study the structure of such spacesH and questions of existence, uniqueness, stability, and minimality under perturbation. In caseZ = 0,H is a Banach manifold locally diffeomorphic to a submanifold of the product of the boundary data space with a finite-dimensional space of Jacobi fields with controlled singular behavior. In this smooth case, the projection ofu εH tou |ϖΩ is Fredholm of index 0. R. H.’s research partially supported by the National Science Foundation. |
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Keywords: | KeywordHeading" >Math Subject Classification 58E20 35J60 58D15 |
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