TY - JOUR
T1 - Harmonic maps with prescribed singularities into Hadamard manifolds
AU - Weinstein, Gilbert
PY - 1996
Y1 - 1996
N2 - Let M a Riemannian manifold of dimension m ≥ 3, let Σ be a closed smooth submanifold of M of co-dimension at least 2, and let H be a Hadamard manifold with pinched sectional curvatures. We prove the existence and uniqueness of harmonic maps φ. M \ Σ → H with prescribed singularities along Σ. When M = ℝ3, and H = Hkℂ, the complex hyperbolic space, this result has applications to the problem of multiple co-axially rotating black holes in general relativity.
AB - Let M a Riemannian manifold of dimension m ≥ 3, let Σ be a closed smooth submanifold of M of co-dimension at least 2, and let H be a Hadamard manifold with pinched sectional curvatures. We prove the existence and uniqueness of harmonic maps φ. M \ Σ → H with prescribed singularities along Σ. When M = ℝ3, and H = Hkℂ, the complex hyperbolic space, this result has applications to the problem of multiple co-axially rotating black holes in general relativity.
KW - Hadamard manifolds
KW - Harmonic maps
KW - Rotating black holes
KW - Singularities
UR - http://www.scopus.com/inward/record.url?scp=0030300396&partnerID=8YFLogxK
U2 - 10.4310/MRL.1996.v3.n6.a11
DO - 10.4310/MRL.1996.v3.n6.a11
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AN - SCOPUS:0030300396
SN - 1073-2780
VL - 3
SP - 835
EP - 844
JO - Mathematical Research Letters
JF - Mathematical Research Letters
IS - 6
ER -