On the structure of conformally compact Einstein metrics

Michael T. Anderson

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On the structure of conformally compact Einstein metrics

Michael T. Anderson

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Abstract

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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Michael T. Anderson. 2010-03-14. On the structure of conformally compact Einstein metrics. https://arxiv.org/abs/math/0402198

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