PROOF OF THE RIGIDITY OF HYPERBOLIC SPACES USING QUASILOCAL MASS TYPE THEOREMS

DOI10.1142/S0219891605000543zbMath1084.53038MaRDI QIDQ5314534

Pengzi Miao

Publication date: 5 September 2005

Published in: Journal of Hyperbolic Differential Equations (Search for Journal in Brave)

zbMATH Keywords

rigidityhyperbolic spaceconformally compact manifold

Mathematics Subject Classification ID

Hyperbolic and elliptic geometries (general) and generalizations (51M10) Rigidity results (53C24)

Cites Work

• Einstein metrics with prescribed conformal infinity on the ball
• On the proof of the positive mass conjecture in general relativity
• Scalar curvature rigidity of asymptotically hyperbolic spin manifolds
• Scalar curvature rigidity for asymptotically locally hyperbolic manifolds
• A definition of total energy-momenta and the positive mass theorem on asymptotically hyperbolic 3-manifolds. I
• Positive mass theorem and the boundary behaviors of compact manifolds with nonnegative scalar curvature.
• Sectional curvature rigidity of asymptotically locally hyperbolic manifolds
• The mass of asymptotically hyperbolic Riemannian manifolds.
• On the uniqueness of AdS space-time in higher dimensions
• The spectrum of an asymptotically hyperbolic Einstein manifold

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