On the Dirichlet problem for harmonic maps with prescribed singularities

Abstract

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.