Mass Rigidity for Hyperbolic Manifolds

We prove the rigidity of the positive mass theorem for asymptotically hyperbolic manifolds. Namely, if the mass equality p 0 = p 1 2 + ⋯ + p n 2 holds, then the manifold is isometric to hyperbolic space. The result was previously proven for spin manifolds (Andersson and Dahl in Ann Glob Anal Geom 16...

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Bibliographic Details
Published in:Communications in mathematical physics 2020-06, Vol.376 (3), p.2329-2349
Main Authors: Huang, Lan-Hsuan, Jang, Hyun Chul, Martin, Daniel
Format: Article
Language:English
Subjects:
Asymptotic properties
Classical and Quantum Gravitation
Complex Systems
Manifolds
Mathematical and Computational Physics
Mathematical Physics
Physics
Physics and Astronomy
Quantum Physics
Relativity Theory
Rigidity
Theoretical
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Summary:We prove the rigidity of the positive mass theorem for asymptotically hyperbolic manifolds. Namely, if the mass equality p 0 = p 1 2 + ⋯ + p n 2 holds, then the manifold is isometric to hyperbolic space. The result was previously proven for spin manifolds (Andersson and Dahl in Ann Glob Anal Geom 16(1):1–2, 1998; Chruściel and Herzlich in Pac J Math 212(2):231–264, 2003; Min-Oo in Math Ann 285(4):527–539; 1989, Wang in J Differ Geom 57(2):273–299, 2001) or under special asymptotics (Andersson et al. in Ann. Henri Poincaré 9(1):1–33, 2008).
ISSN:0010-3616
1432-0916
DOI:10.1007/s00220-019-03623-0