https://neckpinch.com/authors/marco-pozzetta/New arXiv papers by Marco Pozzetta, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2411.06462/arxiv:2411.06462Sun, 10 Nov 2024 00:00:00 GMTLuca Benatti, Alessandra Pluda, Marco Pozzetta — We rigorously show that a large family of monotone quantities along the weak inverse mean curvature flow is the limit case of the corresponding ones along the level sets of p-capacitary potentials. Such monotone quantities include Willmore and Minkowski-type functionals on Riemannian manifolds with nonnegative Ricci curvature. In 3-dimensional manifolds with nonnegative scalar curvature, we also recover the monotonicity of the Hawking mass and its nonlinear potential theoretic counterparts. This unified view is built on a refined analysis of p-capacitary potentials. We prove that they strongly converge in W^(1,q)ₗoc as p→ 1⁺ to the inverse mean curvature flow and their level sets are curvature varifolds. Finally, we also deduce a Gauss-Bonnet-type theorem for level sets of p-capacitary potentials.Mean curvature flowOther curvature flowsInverse mean curvature flowScalar curvatureWeak & singular flowsPhysics https://neckpinch.com/papers/2403.15972/arxiv:2403.15972Sun, 24 Mar 2024 00:00:00 GMTGioacchino Antonelli, Mattia Fogagnolo, Stefano Nardulli, Marco Pozzetta — This paper deals with quasi-local isoperimetric versions of the positive mass theorem on 3-manifolds endowed with continuous complete metrics having nonnegative scalar curvature in a suitable weak sense. As a corollary, we derive existence results for isoperimetric sets in such low regularity setting. Our main tool is a new local version of the weak inverse mean curvature flow enjoying C⁰-stable quantitative estimates.Mean curvature flowOther curvature flowsInverse mean curvature flowScalar curvatureGeometric inequalitiesPhysics