Mass rigidity for hyperbolic manifolds

Abstract

We prove the rigidity of positive mass theorem for asymptotically hyperbolic manifolds. Namely, if the mass equality holds, then the manifold is isometric to hyperbolic space. The result was previously proven for spin manifolds or under special asymptotics.

arXiv commentAppeared in Comm. Math. Phys

References in corpus (5)

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• Equality in the Spacetime Positive Mass Theorem
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• Spacetime Harmonic Functions and Applications to Mass
• Dihedral rigidity of parabolic polyhedrons in hyperbolic spaces
• Positive mass theorems for asymptotically hyperbolic Riemannian manifolds with boundary
• Constructing electrically charged Riemannian manifolds with minimal boundary, prescribed asymptotics, and controlled mass
• The Positive Energy Theorem for Asymptotically Hyperboloidal Initial Data Sets With Toroidal Infinity and Related Rigidity Results
• Positivity of holographic energy
• Asymptotically Hyperbolic Einstein Constraint Equations with Apparent Horizon Boundary and the Penrose Inequality for Perturbations of Schwarzschild-AdS
• Hyperbolic positive energy theorems