Harmonic Maps with Prescribed Singularities on Unbounded Domains

Details Harmonic Maps with Prescribed Singularities on Unbounded Domains Harmonic Maps with Prescribed Singularities on Unbounded Domains

1995-09-19

arxiv.org/abs/dg-ga/9509003v1

Mathematical Research Letters Volume 3, Issue 6, November 1996 pp. 835-844

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

LaTeX2e (amsart) with packages: amssymb, euscript, xspace, 11 pages

Scientific paper

The Einstein/Abelian-Yang-Mills Equations reduce in the stationary and axially symmetric case to a harmonic map with prescribed singularities $\p\colon\R^3\sm\Sigma\to\H^{k+1}_\C$ into the $(k+1)$-dimensional complex hyperbolic space. In this paper, we prove the existence and uniqueness of harmonic maps with prescribed singularities $\p\colon\R^n\sm\Sigma\to\H$, where $\Sigma$ is an unbounded smooth closed submanifold of $\R^n$ 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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