https://neckpinch.com/authors/alessandra-pluda/New arXiv papers by Alessandra Pluda, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT 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/2411.06462arxiv: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://arxiv.org/abs/2207.03879arxiv:2207.03879Fri, 08 Jul 2022 00:00:00 GMTCarlo Mantegazza, Matteo Novaga, Alessandra Pluda — The motion by curvature of networks is the generalization to finite union of curves of the curve shortening flow. This evolution has several peculiar features, mainly due to the presence of junctions where the curves meet. In this paper we show that whenever the length of one single curve vanishes and two triple junctions coalesce, then the curvature of the evolving networks remains bounded. This topological singularity is exclusive of the network flow and it can be referred as a Type-0 singularity, in contrast to the well known Type-I and Type-II ones of the usual mean curvature flow of smooth curves or hypersurfaces, characterized by the different rates of blow up of the curvature. As a consequence, we are able to give a complete description of the evolution of tree-like networks till the first singular time, under the assumption that all the tangents flows have unit multiplicity. If the lifespan of such solutions is finite, then the curvature of the network remains bounded and we can apply the results by Ilmanen-Neves-Schulze/Lira-Mazzeo-Pluda-Saez to restart the flow after the singularity.Mean curvature flowCurve shorteningSingularitiesPhase fields & multiphase flows