Research profile
Works on anisotropic & nonlocal flows, mean curvature flow and singularities.
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Their work in this field since 2016, with the older papers the site recommends. Titles open each paper's page, with its abstract, PDF and HTML versions; Connections shows the papers closest to it. The arXiv listing has the complete record.
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.
In this paper we consider the evolution of sets by a fractional mean curvature flow. Our main result states that for any dimension , there exists an embedded surface in evolving by fractional mean curvature flow, which developes a singularity before it can shrink to a point. When this result generalizes the analogue result of Grayson for the classical mean curvature flow. Interestingly, when , 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.
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NP-RC-724446 is Eleonora Cinti's permanent number in the Ricci flow community on Neckpinch. It stays with them through any change of name or post. More about these numbers.
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