GRG Editor's Choice: Almost rigidity of the positive mass theorem for asymptotically hyperbolic manifolds with spherical symmetry

Sakovich, A. & Sormani, C., Gen Relativ Gravit (2017) 49: 125. https://doi.org/10.1007/s10714-017-2291-y

Open Access | Editor's Choice (Research Article)

First Online: 30 August 2017

"This is a beautifully written paper on the stability of the positive mass theorem for asymptotically hyperbolic manifolds. The authors did a fantastic job at presenting very interesting results. The analogous question has been intensely studied in the Euclidean case. Although the paper is for the special case of rotational symmetry, this is the first paper that addresses this fundamental question in the hyperbolic setting using the intrinsic flat distance."

Abstract:

We use the notion of intrinsic flat distance to address the almost rigidity of the positive mass theorem for asymptotically hyperbolic manifolds. In particular, we prove that a sequence of spherically symmetric asymptotically hyperbolic manifolds satisfying the conditions of the positive mass theorem converges to hyperbolic space in the intrinsic flat sense, if the limit of the mass along the sequence is zero.

The authors:

Dr. Anna Sakovich is an Associate Senior Lecturer at the Department of Mathematics, Uppsala University, Sweden. Dr. Christina Sormani is a Full Professor at the Department of Mathematics, Lehman College, and faculty member of CUNY Graduate Center, New York, USA.

GRG Editor's Choice:

In each volume of GRG, a few papers are marked as “Editor’s Choice”. The primary criteria is original, high quality research that is of wide interest within the community.