May 2023 Local entropy and generic multiplicity one singularities of mean curvature flow of surfaces
Ao Sun
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J. Differential Geom. 124(1): 169-198 (May 2023). DOI: 10.4310/jdg/1685121322

Abstract

In this paper we prove that the generic singularities of mean curvature flow of closed embedded surfaces in $\mathbb{R}^3$ modelled by closed self-shrinkers with multiplicity has multiplicity one. Together with the previous result by Colding–Minicozzi in [CM12], we conclude that the only generic singularity of mean curvature flow of closed embedded surfaces in $\mathbb{R}^3$ modelled by closed self-shrinkers is a multiplicity one sphere. We also construct particular perturbations of the flow to avoid those singularities with multiplicity higher than one. Our result partially addresses the well-known multiplicity one conjecture by Ilmanen.

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Ao Sun. "Local entropy and generic multiplicity one singularities of mean curvature flow of surfaces." J. Differential Geom. 124 (1) 169 - 198, May 2023. https://doi.org/10.4310/jdg/1685121322

Information

Received: 13 November 2018; Accepted: 20 July 2021; Published: May 2023
First available in Project Euclid: 26 May 2023

Digital Object Identifier: 10.4310/jdg/1685121322

Rights: Copyright © 2023 Lehigh University

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Vol.124 • No. 1 • May 2023
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