ROUGH SOLUTIONS OF THE EINSTEIN CONSTRAINT EQUATIONS ON COMPACT MANIFOLDS

Abstract

We construct low regularity solutions of the vacuum Einstein constraint equations on compact manifolds. On 3-manifolds we obtain solutions with metrics in H s where s > 3/2. The constant mean curvature (CMC) conformal method leads to a construction of all CMC initial data with this level of regularity. These results extend a construction from [10] that treated the asymptotically Euclidean case.