Genus one singularities in mean curvature flow

2023/08/11 by Adrian Chun-Pong Chu, Chu, Adrian Chun-Pong, Ao Sun +1 · 2 citations
Mathematics · #Geometric Analysis and Curvature Flows #Mathematical Dynamics and Fractals #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2308.05923

Abstract

We show that for certain one-parameter families of initial conditions in \mathbb R³, when we run mean curvature flow, a genus one singularity must appear in one of the flows. Moreover, such a singularity is robust under perturbation of the family of initial conditions. This contrasts sharply with the case of just a single flow. As an application, we construct an embedded, genus one self-shrinker with entropy lower than a shrinking doughnut.

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