Analysis Seminar

Adrian ChuUniversity of Chicago
Genus one singularities in mean curvature flow

Monday, April 22, 2024 - 2:30pm
Malott 406

This talk will be a continuation of Ao Sun’s. Via an interpolation argument, we show that for certain one-parameter families of initial conditions in ℝ^3, 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.