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Article Dans Une Revue Communications in Mathematical Physics Année : 2014

Asymptotically hyperbolic manifolds with small mass

Résumé

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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Dates et versions

hal-00783618 , version 1 (27-01-2024)

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