Singular Harmonic Maps and Applications to General Relativity
Singular Harmonic Maps and Applications to General Relativity
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奇异调和图及其在广义相对论中的应用
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发表时间：
2011
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通讯作者：
Luc Nguyen
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作者：
Luc Nguyen
对轴对称静止多黑洞构型和同轴旋转黑洞间的作用力的研究，首先需要分析所谓的约化奇异调和映象的“边界正则性”。我们通过将这些调和映射看作是一些具有奇异系数的齐次散度系统的解来进行这种分析。我们的结果推广了Weinstein(Comm Pure Appl Math 43：903-948,1990；Comm Pure Appl Math 45：1183-1203,1992)和Li和Tian(Manu Math 73(1)：83-89,1991；Commun Math Phys 149：1-30,1992；微分几何：PDE on流形，第54卷，317-326页，1993)的工作。本文基于作者的博士论文(到双曲空间的奇异调和映射及其在广义相对论中的应用，新泽西州立大学罗格斯分校博士论文，2009)。
The study of axially symmetric stationary multi-black-hole configurations and the force between co-axially rotating black holes involves, as a first step, an analysis on the “boundary regularity” of the so-called reduced singular harmonic maps. We carry out this analysis by considering those harmonic maps as solutions to some homogeneous divergence systems of partial differential equations with singular coefficients. Our results extend previous works by Weinstein (Comm Pure Appl Math 43:903–948, 1990; Comm Pure Appl Math 45:1183–1203, 1992) and by Li and Tian (Manu Math 73(1):83–89, 1991; Commun Math Phys 149:1–30, 1992; Differential geometry: PDE on manifolds, vol 54, pp. 317–326, 1993). This paper is based on the Ph.D. thesis of the author (Singular harmonic maps into hyperbolic spaces and applications to general relativity, PhD thesis, The State University of New Jersey, Rutgers, 2009).