https://neckpinch.com/authors/lorenzo-mazzieri/New arXiv papers by Lorenzo Mazzieri, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2212.10215arxiv:2212.10215Tue, 20 Dec 2022 00:00:00 GMTLuca Benatti, Mattia Fogagnolo, Lorenzo Mazzieri — We prove that the Riemannian Penrose Inequality holds for Asymptotically Flat 3-manifolds with nonnegative scalar curvature and connected horizon boundary, provided the optimal decay assumptions are met, which result in the ADM mass being a well-defined geometric invariant. Our proof builds on a novel interplay between the Hawking mass and a potential-theoretic version of it, recently introduced by Agostiniani, Oronzio and the third named author. As a consequence, we establish the equality between ADM mass and Huisken's Isoperimetric mass under the above sharp assumptions. Moreover, we establish a Riemannian Penrose Inequality in terms of the Isoperimetric mass on any 3-manifold with nonnegative scalar curvature, connected horizon boundary, and which supports a well-posed notion of weak Inverse Mean Curvature Flow. In particular, such Isoperimetric Riemannian Penrose Inequality does not require the asymptotic flatness of the manifold. The argument is based on a new asymptotic comparison result involving Huisken's Isoperimetric mass and the Hawking mass.Mean curvature flowOther curvature flowsInverse mean curvature flowScalar curvatureBoundaries & non-compactGeometric inequalitiesPhysics https://arxiv.org/abs/2207.08607arxiv:2207.08607Mon, 18 Jul 2022 00:00:00 GMTLuca Benatti, Mattia Fogagnolo, Lorenzo Mazzieri — We study the asymptotic behaviour of the p-capacitary potential and of the weak Inverse Mean Curvature Flow of a bounded set along the ends of an Asymptotically Conical Riemannian manifolds with asymptotically nonnegative Ricci curvature.Mean curvature flowOther curvature flowsInverse mean curvature flowBoundaries & non-compact