A variational analysis of Einstein-scalar field Lichnerowicz equations on compact Riemannian manifolds
General Relativity and Quantum Cosmology
2008-11-26 v1 Analysis of PDEs
Differential Geometry
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.
Keywords
Cite
@article{arxiv.gr-qc/0702031,
title = {A variational analysis of Einstein-scalar field Lichnerowicz equations on compact Riemannian manifolds},
author = {Emmanuel Hebey and Frank Pacard and Daniel Pollack},
journal= {arXiv preprint arXiv:gr-qc/0702031},
year = {2008}
}
Comments
15 pages