PDEA Seminar: 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.

Our quantity can be deduced from a reduced Hamiltonian perspective and it is nonincreasing along CMC foliations of asymptotically Milne-like vacuum spacetimes. We present a positive mass theorem for orientable three-manifolds which don’t contain non-separating spheres. In addition, we show 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.

Participate on site or via Zoom link, meeting ID: 67226102216. Ensure Zoom access by contacting the organisers in advance.

This is a seminar in the PDEs and Applications seminar series.