Contents Online
Mathematical Research Letters
Volume 3 (1996)
Number 6
Harmonic Maps with Prescribed Singularities into Hadamard Manifolds
Pages: 835 – 844
DOI: https://dx.doi.org/10.4310/MRL.1996.v3.n6.a11
Author
Abstract
Let $M$ a Riemannian manifold of dimension $m\geq3$, let $\Sigma$ 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 $\varphi\colon M\setminus\Sigma\to H$ with prescribed singularities along $\Sigma$. When $M={\Bbb R}^3$, and $H=H^k_{\Bbb C}$, the complex hyperbolic space, this result has applications to the problem of multiple co-axially rotating black holes in general relativity.
Published 1 January 1996