A variational analysis of einstein-scalar field lichnerowicz equations on compact riemannian manifolds

Emmanuel Hebey; Frank Pacard; Daniel Pollack

doi:10.1007/s00220-007-0377-1

A variational analysis of einstein-scalar field lichnerowicz equations on compact riemannian manifolds

Emmanuel Hebey
, Frank Pacard
, Daniel Pollack

Département de Mathématiques
CY Cergy Paris Université
Université de PARIS XII
Department of Mathematics
University of Washington

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

56 Citations (Scopus)

Résumé

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.

langue originale	Anglais
Pages (de - à)	117-132
Nombre de pages	16
journal	Communications in Mathematical Physics
Volume	278
Numéro de publication	1
Les DOIs	https://doi.org/10.1007/s00220-007-0377-1
état	Publié - 1 févr. 2008
Modification externe	Oui

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10.1007/s00220-007-0377-1

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abstract = "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.",

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AB - 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.

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A variational analysis of einstein-scalar field lichnerowicz equations on compact riemannian manifolds

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