Harmonic maps with fixed singular sets
Harmonic maps with fixed singular sets
复制标题
具有固定奇异集的调和映射
DOI：
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发表时间：
1992
期刊：
影响因子：
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通讯作者：
Libin Mou
中科院分区：
文献类型：
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作者：
R. Hardt;Libin Mou
设Ω是Rm中的光滑域，N是紧的光滑黎曼流形，z是Ω的具有有限(m−3)维Minkowski含量的固定紧子集(例如，Z ism−3可正)。我们考虑调和映射的各种空间：Ω→N，它们在Z附近有一个奇异集和受控行为。我们研究了这类空间H的结构以及在扰动下的存在性、唯一性、稳定性和极小性问题。在Casez=0中，H是Banach流形，局部微分同胚于边界数据空间与具有受控奇异行为的有限维Jacobi场空间的乘积的子流形。在这种光滑情形下，εH的投影是指数为0的Fredholm型的。
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.