TY - JOUR
T1 - Harmonic maps with prescribed singularities on unbounded domains
AU - Weinstein, Gilbert
PY - 1996/6
Y1 - 1996/6
N2 - The Einstein/Abelian-Yang-Mills Equations reduce in the stationary and axially symmetric case to a harmonic map with prescribed singularities φ: ℝ3\Σ → ℍk+1ℂ into the (k + 1)-dimensional complex hyperbolic space. In this paper, we prove the existence and uniqueness of harmonic maps with prescribed singularities φ: ℝn\Σ → ℍ, where Σ is an unbounded smooth closed submanifold of ℝn 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.
AB - The Einstein/Abelian-Yang-Mills Equations reduce in the stationary and axially symmetric case to a harmonic map with prescribed singularities φ: ℝ3\Σ → ℍk+1ℂ into the (k + 1)-dimensional complex hyperbolic space. In this paper, we prove the existence and uniqueness of harmonic maps with prescribed singularities φ: ℝn\Σ → ℍ, where Σ is an unbounded smooth closed submanifold of ℝn 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.
UR - http://www.scopus.com/inward/record.url?scp=0011419569&partnerID=8YFLogxK
U2 - 10.1353/ajm.1996.0029
DO - 10.1353/ajm.1996.0029
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AN - SCOPUS:0011419569
SN - 0002-9327
VL - 118
SP - 689
EP - 700
JO - American Journal of Mathematics
JF - American Journal of Mathematics
IS - 3
ER -