# 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.
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https://hal.archives-ouvertes.fr/hal-00783618
Contributor : Romain Gicquaud <>
Submitted on : Friday, February 1, 2013 - 1:25:59 PM
Last modification on : Thursday, March 5, 2020 - 5:33:43 PM

### Identifiers

• HAL Id : hal-00783618, version 1
• ARXIV : 1209.0154

### 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. ⟨hal-00783618⟩

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