Renormalized volume and non-degeneracy of conformally compact Einstein four-manifolds

DOI10.1016/J.GEOMPHYS.2024.105226zbMATH Open1544.53056MaRDI QIDQ6564589

Matthew J. Gursky

Publication date: 1 July 2024

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

zbMATH Keywords

Einstein metricslinearized Einstein equationsconformally compact manifolds

Mathematics Subject Classification ID

Applications of differential geometry to physics (53Z05) Einstein's equations (general structure, canonical formalism, Cauchy problems) (83C05) Special Riemannian manifolds (Einstein, Sasakian, etc.) (53C25)

Cites Work

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• Boundary regularity of conformally compact Einstein metrics
• Ricci deformation of the metric on a Riemannian manifold
• Einstein metrics with prescribed conformal infinity on the ball
• The Yamabe problem on manifolds with boundary
• Boundary regularity, uniqueness and non-uniqueness for AH Einstein metrics on 4-manifolds.
• Four-manifolds with \(\delta W^+=0\) and Einstein constants of the sphere.
• Non-existence of Poincaré-Einstein manifolds with prescribed conformal infinity
• On non-degeneracy of Riemannian Schwarzschild-anti de Sitter metrics
• The Functional Determinant of a Four-Dimensional Boundary Value Problem
• Fredholm operators and Einstein metrics on conformally compact manifolds
• \(L^2\) curvature and volume renormalization of AHE metrics on 4-manifolds

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