On the structure of conformally compact Einstein metrics

Details On the structure of conformally compact Einstein metrics On the structure of conformally compact Einstein metrics

2004-02-12

arxiv.org/abs/math/0402198v5

Mathematics

Differential Geometry

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Scientific paper

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.

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