On the Dirichlet problem for harmonic maps with prescribed singularities

Details On the Dirichlet problem for harmonic maps with prescribed singularities On the Dirichlet problem for harmonic maps with prescribed singularities

1994-08-26

arxiv.org/abs/dg-ga/9408005v1

Duke Math. J. Volume 77, Number 1 (1995), 135-165

Mathematics

Differential Geometry

28 pages

Scientific paper

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.

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