| HARMONIC MAPS WITH PRESCRIBED SINGULARITIES INTO HADAMARD MANIFOLDS (2008) | |||||||||||||
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| Abstract. Let M a Riemannian manifold of dimension m ≥ 3, let Σ 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 ϕ: M \ Σ → H with prescribed singularities along Σ. When M = � 3, and H = H k C, the complex hyperbolic space, this result has applications to the problem of multiple co-axially rotating black holes in general relativity. 1. | |||||||||||||
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