  The main result of this paper is that the space of conformally compact
Einstein metrics on a given manifold is a smooth, infinite dimensional Banach
manifold, provided it is non-empty, generalizing earlier work of Graham-Lee and
Biquard. We also prove full boundary regularity for such metrics in dimension
4, and a local existence and uniqueness theorem for such metrics with
prescribed metric and stress-energy tensor at conformal infinity, again in
dimension 4. This result also holds for Lorentzian-Einstein metrics with a
positive cosmological constant.
