On the Dirichlet problem for harmonic maps with prescribed singularities
On the Dirichlet problem for harmonic maps with prescribed singularities
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关于具有规定奇点的调和映射的狄利克雷问题
DOI：
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发表时间：
1994
期刊：
影响因子：
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通讯作者：
Gilbert Weinstein
中科院分区：
文献类型：
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作者：
Gilbert Weinstein
设$M$是一个秩为1的非紧型经典黎曼全局对称空间。我们证明了具有给定奇异点的调和映射到$M$的Dirichlet问题的解的存在唯一性。这推广了我们之前的工作，其中这种映射到双曲平面被构造。在M为复双曲平面的情况下，这个问题可以应用于广义相对论中同轴旋转带电黑洞的平衡构型。
Let $M$ be a classical Riemannian globally symmetric space of rank one and non-compact type. We prove the existence and uniqueness of solutions to the Dirichlet problem for harmonic maps into $M$ with prescribed singularities along a closed submanifold of the domain. This generalizes our previous work where such maps into the hyperbolic plane were constructed. This problem, in the case where $M$ is the complex-hyperbolic plane, has applications to equilibrium configurations of co-axially rotating charged black holes in General Relativity.