Harmonic Maps with Prescribed Singularities into Hadamard Manifolds
Harmonic Maps with Prescribed Singularities into Hadamard Manifolds
复制标题
哈达玛流形中具有规定奇点的调和映射
DOI：
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发表时间：
1996
期刊：
影响因子：
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通讯作者：
G. Weinstein
中科院分区：
文献类型：
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作者：
G. Weinstein
设M为维数M≥3的黎曼流形，设Σ为协维数至少为2的M的光滑闭子流形，设H为截曲率缩紧的Hadamard流形。证明了沿Σ具有规定奇异点的调和映射φ: M \ Σ→H的存在唯一性。当复双曲空间M = R, H = hc时，该结果适用于广义相对论中多个共轴旋转黑洞的问题。
Let M a Riemannian manifold of dimension m ≥ 3, let Σ be a closed smooth submanifold of M of co-dimension at least 2, and let H be a Hadamard manifold with pinched sectional curvatures. We prove the existence and uniqueness of harmonic maps φ : M \ Σ → H with prescribed singularities along Σ. When M = R, and H = H C , the complex hyperbolic space, this result has applications to the problem of multiple co-axially rotating black holes in general relativity.