Regularity of harmonic maps with prescribed singularities
type: Item
instance of: scholarly article
title: Regularity of harmonic maps with prescribed singularities
zbMATH Open document ID: 0785.53047
DOI: 10.1007/BF02096622
published in: Communications in Mathematical Physics
publication date: 1993-01-16T00:00:00Z
review text: Let \(M\) be a complete Riemannian manifold and \(N\) a codimension two closed submanifold. Given a smooth map \(h: M\setminus N\to \overline{H^ m}\) into the naturally compactified hyperbolic space \(H^ m\), the authors show the existence of a harmonic map \(\varphi: M\setminus N\to H^ m\) with similar asymptotic behaviour to \(h\) along \(N\). Here, `similar behavior' means that, in terms of the coordinate functions \(h_ 1,\dots,h_ m\) of \(h\) in the upper half-space model of \(H^ m\), \(\varphi\) is of the form \((\varphi_ 1,\dots,\varphi_{m-1},h_ me^{\varphi_ m})\), with \(\varphi_ i-h_ i\) belonging to a suitable completion of \(C^ \infty_ 0(M)\) or \(C^ \infty_ 0(M\setminus N)\). This is then used to give a partial solution to the Hawking's conjecture to the effect that there is no asymptotically flat axially symmetric solution to the Einstein Vacuum Equation with disconnected event horizon of small angular momentum.
Mathematics Subject Classification ID: 53C40
Mathematics Subject Classification ID: 58E20
Mathematics Subject Classification ID: 83C57
zbMATH DE Number: 95693
zbMATH Keywords: hyperbolic space
zbMATH Keywords: similar asymptotic behaviour
zbMATH Keywords: Hawking's conjecture
author: Yan Yan Li
author: Gang Tian
reviewed by: Gábor Tóth
MaRDI profile type: Publication
cites work: Harmonic Mappings of Riemannian Manifolds
cites work: On the regularity of the minima of variational integrals
cites work: Harmonic maps of manifolds with boundary
cites work: Mappings minimizing theLp norm of the gradient
cites work: Q4123700
cites work: Nonexistence of axially symmetric, stationary solution of Einstein vacuum equation with disconnected symmetric event horizon
cites work: Applications harmoniques de surfaces riemanniennes
cites work: The existence of minimal immersions of 2-spheres
cites work: A regularity theory for harmonic maps
cites work: Boundary regularity and the Dirichlet problem for harmonic maps
cites work: Existence of incompressible minimal surfaces and the topology of three dimensional manifolds with non-negative scalar curvature
cites work: On rotating black holes in equilibrium in general relativity
Wikidata QID: Q126021121
full work available at URL: https://doi.org/10.1007/bf02096622
OpenAlex ID: W1989464477
description: scientific article; zbMATH DE number 95693