HARMONIC MAPS WITH PRESCRIBED SINGULARITIES ON UNBOUNDED-DOMAINS

The Einstein/Abelian-Yang-Mills Equations reduce in the stationary and axially symmetric case to a harmonic map with prescribed singularitie s phi: R(3)\Sigma --> H-C(k+1) into the (k + 1)-dimensional complex hy perbolic space. In this paper, we prove the existence and uniqueness o f harmonic maps with prescribed singularities phi: R(n)\Sigma --> H wh ere Sigma is an unbounded smooth closed submanifold of R(n) of codimen sion at least 2, and H is a real, complex, or quaternionic hyperbolic space. As a corollary, we prove the existence of solutions to the redu ced stationary and axially symmetric Einstein/Abelian-Yang-Mills Equat ions.