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- Title
Harmonic maps with fixed singular sets.
- Authors
Hardt, Robert; Mou, Libin
- Abstract
Suppose Ω is a smooth domain in R, N is a compact smooth Riemannian manifold, and Z is a fixed compact subset of Ω having finite ( m − 3)-dimensional Minkowski content (e.g., Z is m − 3 rectifiable). We consider various spaces of harmonic maps u: Ω → N that have a singular set Z and controlled behavior near Z. We study the structure of such spaces H and questions of existence, uniqueness, stability, and minimality under perturbation. In case Z = 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 of u ε H to u ¦ϖΩ is Fredholm of index 0.
- Publication
Journal of Geometric Analysis, 1992, Vol 2, Issue 5, p445
- ISSN
1050-6926
- Publication type
Article
- DOI
10.1007/BF02921301