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# Asymptotically hyperbolic manifolds with small mass

Abstract : 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.
Document type :
Journal articles
Domain :

https://hal.archives-ouvertes.fr/hal-00783618
Contributor : Romain Gicquaud Connect in order to contact the contributor
Submitted on : Friday, February 1, 2013 - 1:25:59 PM
Last modification on : Tuesday, March 1, 2022 - 1:38:48 PM

### Citation

Mattias Dahl, Romain Gicquaud, Anna Sakovich. Asymptotically hyperbolic manifolds with small mass. Communications in Mathematical Physics, Springer Verlag, 2014, 325 (2), pp.757-801. ⟨10.1007/s00220-013-1827-6⟩. ⟨hal-00783618⟩

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