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Geometric Analysis Seminar

Genus one singularities in mean curvature flow

Ao Sun (Lehigh)

Location:  Hill-705
Date & time: Tuesday, 07 November 2023 at 2:50PM - 3:50PM

Abstract: We show that for certain one-parameter families of initial conditions in 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. Among applications, we construct an embedded, genus one self-shrinker with entropy lower than a shrinking doughnut, and we proved that the fourth lowest entropy self-shrinker in R3 can not be rotationally symmetric. Based on joint work with Adrian Chu.

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