On boundary value problems for Einstein metrics

On any given compact manifold M nC1 with boundary @M , it is proved that the moduli space E of Einstein metrics on M , if non-empty, is a smooth, infinite dimensional Banach manifold, at least when 1 .M; @M / D 0. Thus, the Einstein moduli space is unobstructed. The usual Dirichlet and Neumann boundary maps to data on @M are smooth, but not Fredholm. Instead, one has natural mixed boundaryvalue problems which give Fredholm boundary maps.