Mathematical Research Letters

Volume 3 (1996)

Number 6

Harmonic Maps with Prescribed Singularities into Hadamard Manifolds

Pages: 835 – 844



Gilbert Weinstein (University of Alabama at Birmingham)


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.

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