| Harmonic Maps With Prescribed Singularities Into Hadamard Manifolds (1997) | |||||||||||||
Abstract | |||||||||||||
| . Let M a Riemannian manifold of dimension m ? 3, 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 ' : M n \Sigma ! H with prescribed singularities along \Sigma. When M = R 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. Introduction In [We3, We4], we showed how the Einstein/Abelian-Yang-Mills equations, under the assumptions of stationarity, axial symmetry, asymptotic flatness, together with regularity and non-degeneracy conditions, are equivalent to a harmonic map problem with prescribed singularities into the complex hyperbolic space H k C = SU(1; k)=S(U(1) \Theta U(k)). We then used a variational method to prove the existence of such harmonic maps with prescribed singularities into any hyperbolic space, H k K wh... | |||||||||||||
Publication details | |||||||||||||
| |||||||||||||