https://neckpinch.com/authors/eleonora-cinti/New arXiv papers by Eleonora Cinti, from Neckpinch Tue, 10 Nov 2026 04:10:28 GMT https://neckpinch.com/papers/1811.08651/arxiv:1811.08651Wed, 21 Nov 2018 00:00:00 GMTEleonora Cinti, Carlo Sinestrari, Enrico Valdinoci — We consider the volume preserving geometric evolution of the boundary of a set under fractional mean curvature. We show that smooth convex solutions maintain their fractional curvatures bounded for all times, and the long time asymptotics approach round spheres. The proofs are based on apriori estimates on the inner and outer radii of the solutions.Mean curvature flowAnisotropic & nonlocal flows https://neckpinch.com/papers/1607.08032/arxiv:1607.08032Wed, 27 Jul 2016 00:00:00 GMTEleonora Cinti, Carlo Sinestrari, Enrico Valdinoci — In this paper we consider the evolution of sets by a fractional mean curvature flow. Our main result states that for any dimension n > 2, there exists an embedded surface in ℝⁿ evolving by fractional mean curvature flow, which developes a singularity before it can shrink to a point. When n > 3 this result generalizes the analogue result of Grayson for the classical mean curvature flow. Interestingly, when n = 2, our result provides instead a counterexample in the nonlocal framework to the well known Grayson Theorem, which states that any smooth embedded curve in the plane evolving by (classical) MCF shrinks to a point.Mean curvature flowAnisotropic & nonlocal flowsSingularities