https://neckpinch.com/authors/mattia-fogagnolo/New arXiv papers by Mattia Fogagnolo, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2610.38929arxiv:2610.38929Wed, 28 Oct 2026 00:00:00 GMTGaia Bombardieri, Mattia Fogagnolo, Valentina Franceschi — We study the arrival time equation of the mean-convex horizontal mean curvature flow in the Heisenberg group. We prove existence of viscosity solutions when the initial set is horizontally mean-convex and either non-characteristic, or axisymmetric and with horizontal mean curvature extending continuously across the characteristic set. A key ingredient is an approximation scheme by sets with prescribed Riemannian mean curvature, which preserves the mean-curvature bounds up to an arbitrarily small error. We further show that, when the evolving level sets form a generalized C²-foliation, the horizontal mean curvature blows up around characteristic points. This provides an obstruction to self-similar evolution in the axisymmetric class considered above and, in particular, shows that the Pansu sphere cannot evolve self-similarly.Mean curvature flowWeak & singular flows https://arxiv.org/abs/2605.20114arxiv:2605.20114Tue, 19 May 2026 00:00:00 GMTMattia Fogagnolo, Giorgio Gatti, Alessandra Pluda — We propose a notion of scalar curvature lower bounds in a three-dimensional Riemannian manifold endowed with a C⁰ metric based on the monotonicity of the Hawking mass along the inverse mean curvature flow. We present a stability theorem for continuous Riemannian metrics with nonnegative scalar curvature in such IMCF sense.Mean curvature flowOther curvature flowsInverse mean curvature flow3-manifoldsScalar curvatureStability & uniquenessPhysics https://arxiv.org/abs/2403.15972arxiv: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 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