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On the structure of conformally compact Einstein metrics

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Abstract

Let M be an (n + 1)-dimensional manifold with non-empty boundary, satisfying π 1(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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Authors and Affiliations

  1. Department of Mathematics, S.U.N.Y. at Stony Brook, Stony Brook, NY, 11794-3651, USA

    Michael T. Anderson

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  1. Michael T. Anderson
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Correspondence to Michael T. Anderson.

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Communicated by G. Huisken.

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Anderson, M.T. On the structure of conformally compact Einstein metrics. Calc. Var. 39, 459–489 (2010). https://doi.org/10.1007/s00526-010-0320-8

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  • DOI: https://doi.org/10.1007/s00526-010-0320-8

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