Harmonic maps with prescribed singularities into Hadamard manifolds (Q676127)

The equivalence of Einstein/Abelian-Yang-Mills equations to the harmonic map problem with prescribed singularities into a complex hyperbolic space was shown in some previous papers of the author [Commun. Partial Differ. Equations 21, No. 9-10, 1389-1430 (1996; Zbl 0863.53061) and Am. J. Math. 118, No. 3, 689-700 (1996; Zbl 0858.53018)]. A generalization of this result is given in this paper. Let \(M\) be a Riemannian manifold of dimension \(m\geq 3\), let \(\Sigma\) be a closed smooth submanifold of \(M\) of codimension at least 2, and let \(H\) be a Hadamard manifold with pinched sectional curvatures (PSC's). The existence and uniqueness of harmonic maps \(\varphi:M\setminus \Sigma\to H\) is proven for any target \(H\) with PSC's \(-b^2\leq k\leq-a^2<0\). The results are applied to the problem of multiple coaxially rotating black holes in general relativity.