Applications of Fixed Point Theorems to the Vacuum Einstein Constraint Equations with Non-Constant Mean Curvature
Mathematical Physics
2015-11-10 v3 General Relativity and Quantum Cosmology
Analysis of PDEs
Differential Geometry
math.MP
Abstract
In this paper, we introduce new methods for solving the vacuum Einstein constraints equations: the first one is based on Schaefer's fixed point theorem (known methods use Schauder's fixed point theorem) while the second one uses the concept of half-continuity coupled with the introduction of local supersolutions. These methods allow to: unify some recent existence results, simplify many proofs (for instance, the main theorem in arXiv:1012.2188) and weaken the assumptions of many recent results.
Keywords
Cite
@article{arxiv.1405.7731,
title = {Applications of Fixed Point Theorems to the Vacuum Einstein Constraint Equations with Non-Constant Mean Curvature},
author = {Nguyen The Cang},
journal= {arXiv preprint arXiv:1405.7731},
year = {2015}
}
Comments
In this version, I change from 3-dimensional case to n-dimensional case