A variational analysis of Einstein-scalar field Lichnerowicz equations on compact Riemannian manifolds

被引：49

作者：

Hebey, Emmanuel ^{[1
]}

Pacard, Frank ^{[2
]}

Pollack, Daniel ^{[3
]}

机构：

[1] Univ Cergy Pontoise, Dept Math, F-95302 Cergy Pontoise, France

[2] Univ Paris 12, Dept Math, F-94010 Creteil, France

[3] Univ Washington, Dept Math, Seattle, WA 98195 USA

来源：

COMMUNICATIONS IN MATHEMATICAL PHYSICS | 2008年 / 278卷 / 01期

关键词：

D O I：

10.1007/s00220-007-0377-1

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We establish new existence and non-existence results for positive solutions of the Einstein-scalar field Lichnerowicz equation on compact manifolds. This equation arises from the Hamiltonian constraint equation for the Einstein-scalar field system in general relativity. Our analysis introduces variational techniques, in the form of the mountain pass lemma, to the analysis of the Hamiltonian constraint equation, which has been previously studied by other methods.

引用

页码：117 / 132

页数：16

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