On the Structure of Conformally Compact Einstein Metrics
نویسنده
چکیده
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 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.
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