Local structure theory of Einstein manifolds with boundary

Abstract: We study local structure of the moduli space of compact Einstein metrics with respect to the boundary conformal metric and mean curvature. In dimension three, we confirm M. Anderson's conjecture in a strong sense, showing that the map from Einstein metrics to such boundary data is generically a local diffeomorphism. In dimensions greater than three, we obtain similar results for Ricci flat metrics and negative Einstein metrics under new non-degenerate boundary conditions.