On the volume-renormalized mass

Abstract: We give an overview on results about a new mass-like quantity on asymptotically hyperbolic manifolds, which was recently introduced by Dahl, McCormick and me. The volume-renormalized mass is essentially a linear combination of the ADM mass surface integral and a renormalization of the volume. It is well-defined and diffeomorphism invariant under weaker fall-off conditions than required to ensure that the renormalized volume and the ADM mass surface integral are well-defined separately. We show that our quantity can be deduced from a reduced Hamiltonian perspective and that it is nonincreasing along CMC foliations of asymptotically Milne-like vacuum spacetimes. We prove a positive mass theorem for orientable three-manifolds which don’t contain non-separating spheres. In addition, we demonstrate that a Poincaré–Einstein manifold is dynamically stable under the Ricci flow if and only if it is a local minimizer of the mass. This talk is based on collaborations with Mattias Dahl, Stephen McCormick, Francesca Oronzio, Alan Pinoy and Louis Yudowitz.

differential geometry

Audience: researchers in the topic

( video )

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Virtual seminar on geometry with symmetries

Series comments: Description: Research seminar in Lie group actions in Differential geometry.

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