%0 Journal Article
%T Applications of Fixed Point Theorems to the Vacuum Einstein Constraint Equations with Non-Constant Mean Curvature
%A Nguyen The Cang
%J Mathematics
%D 2014
%I arXiv
%R 10.1007/s00023-015-0446-5
%X 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.
%U http://arxiv.org/abs/1405.7731v3