Asymptotically Hyperbolic Manifolds with Small Mass

For asymptotically hyperbolic manifolds of dimension n with scalar curvature at least equal to − n ( n − 1) the conjectured positive mass theorem states that the mass is non-negative, and vanishes only if the manifold is isometric to hyperbolic space. In this paper we study asymptotically hyperbolic...

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Bibliographic Details
Published in:Communications in mathematical physics 2014, Vol.325 (2), p.757-801
Main Authors: Dahl, Mattias, Gicquaud, Romain, Sakovich, Anna
Format: Article
Language:English
Subjects:
Classical and Quantum Gravitation
Complex Systems
Differential Geometry
General Relativity and Quantum Cosmology
Mathematical and Computational Physics
Mathematical Physics
Mathematics
Physics
Physics and Astronomy
Quantum Physics
Relativity Theory
Theoretical
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Summary:For asymptotically hyperbolic manifolds of dimension n with scalar curvature at least equal to − n ( n − 1) the conjectured positive mass theorem states that the mass is non-negative, and vanishes only if the manifold is isometric to hyperbolic space. In this paper we study asymptotically hyperbolic manifolds which are also conformally hyperbolic outside a ball of fixed radius, and for which the positive mass theorem holds. For such manifolds we show that the conformal factor tends to one as the mass tends to zero.
ISSN:0010-3616
1432-0916
1432-0916
DOI:10.1007/s00220-013-1827-6