On the structure of conformally compact Einstein metrics

Some Results on the Structure of Conformally Compact Einstein Metrics

The main result of this paper is that the space of conformally compact Einstein metrics on any 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 a...

On the Structure of Conformally Compact Einstein Metrics

LetM be an (n+1)-dimensional manifold with non-empty boundary, satisfying π1(M,∂M) = 0. The main result of this paper is that the space of conformally compact Einstein metrics on M is a smooth, infinite dimensional Banach manifold, provided it is non-empty. We also prove full boundary regularity for such metrics in dimension 4 and a local existence and uniqueness theorem for such metrics with p...

Topics in Conformally Compact Einstein Metrics

Conformal compactifications of Einstein metrics were introduced by Penrose [38], as a means to study the behavior of gravitational fields at infinity, i.e. the asymptotic behavior of solutions to the vacuum Einstein equations at null infinity. This has remained a very active area of research, cf. [27], [19] for recent surveys. In the context of Riemannian metrics, the modern study of conformall...

Fredholm Operators and Einstein Metrics on Conformally Compact Manifolds

The main purpose of this monograph is to give an elementary and self-contained account of the existence of asymptotically hyperbolic Einstein metrics with prescribed conformal infinities sufficiently close to that of a given asymptotically hyperbolic Einstein metric with nonpositive curvature. The proof is based on an elementary derivation of sharp Fredholm theorems for self-adjoint geometric l...

Volume and Area Renormalizations for Conformally Compact Einstein Metrics