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

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	117-132
Number of pages	16
Journal	Communications in Mathematical Physics
Volume	278
Issue number	1
DOIs	https://doi.org/10.1007/s00220-007-0377-1
Publication status	Published - 1 Feb 2008
Externally published	Yes

Access to Document

10.1007/s00220-007-0377-1

Cite this

@article{9d42d3a8d9c846c18233014f89e59aea,

title = "A variational analysis of einstein-scalar field lichnerowicz equations on compact riemannian manifolds",

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.",

author = "Emmanuel Hebey and Frank Pacard and Daniel Pollack",

year = "2008",

month = feb,

day = "1",

doi = "10.1007/s00220-007-0377-1",

language = "English",

volume = "278",

pages = "117--132",

journal = "Communications in Mathematical Physics",

issn = "0010-3616",

number = "1",

}

TY - JOUR

T1 - A variational analysis of einstein-scalar field lichnerowicz equations on compact riemannian manifolds

AU - Hebey, Emmanuel

AU - Pacard, Frank

AU - Pollack, Daniel

PY - 2008/2/1

Y1 - 2008/2/1

N2 - 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.

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.

U2 - 10.1007/s00220-007-0377-1

DO - 10.1007/s00220-007-0377-1

M3 - Article

AN - SCOPUS:38049046222

SN - 0010-3616

VL - 278

SP - 117

EP - 132

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

IS - 1

ER -

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

Abstract

Access to Document

Fingerprint

Cite this