https://neckpinch.com/authors/stephen-mccormick/New arXiv papers by Stephen McCormick, from Neckpinch Tue, 03 Nov 2026 08:37:45 GMT https://neckpinch.com/papers/2307.06196/arxiv:2307.06196Wed, 12 Jul 2023 00:00:00 GMTMattias Dahl, Klaus Kroencke, Stephen McCormick — We define a geometric quantity for asymptotically hyperbolic manifolds, which we call the volume-renormalized mass. It is essentially a linear combination of the ADM mass surface integral and a renormalization of the volume. We show that the volume-renormalized mass 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 prove several positivity results for the volume-renormalized mass. We also use it to define a renormalized Einstein–Hilbert action and a renormalized expander entropy which is nondecreasing under the Ricci flow. Further, we show that local maximizers of the entropy are local minimizers of the volume-renormalized mass.Ricci flowRicci solitonsBoundaries & non-compactPhysics