Harmonic Maps with Prescribed Singularities on Unbounded Domains
نویسنده
چکیده
The Einstein/Abelian-Yang-Mills Equations reduce in the stationary and axially symmetric case to a harmonic map with prescribed singularities φ : R \Σ → H C into the (k+1)-dimensional complex hyperbolic space. In this paper, we prove the existence and uniqueness of harmonic maps with prescribed singularities φ : R \ Σ → H, where Σ is an unbounded smooth closed submanifold of R of codimension at least 2, and H is a real, complex, or quaternionic hyperbolic space. As a corollary, we prove the existence of solutions to the reduced stationary and axially symmetric Einstein/Abelian-Yang-Mills Equations.
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