Applications of Fixed Point Theorems to the Vacuum Einstein Constraint   Equations with Non-Constant Mean Curvature
  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. 
Nguyen The Cang
math-ph gr-qc math.AP math.DG math.MP