On the structure of conformally compact Einstein metrics

2004/02/12 by Michael T. Anderson, Anderson, Michael T. · 1 citation
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Cosmology and Gravitation Theories #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.math/0402198

openalex publication_date 2004/02/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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• Conformal hypersurface invariants and Bach-type Boundary Problems

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• Topics in conformally compact Einstein metrics
• On compactness conformally compact Einstein manifolds and uniqueness of Graham-Lee metrics, III
• Compactness of conformally compact Einstein manifolds in dimension 4
• Einstein metrics with prescribed conformal infinity on 4-manifolds
• Boundary Regularity for Conformally Compact Einstein Metrics in Even Dimensions