Genus one singularities in mean curvature flow
Differential Geometry
2025-12-03 v3 Analysis of PDEs
Geometric Topology
Abstract
We show that for certain one-parameter families of initial conditions in , 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.
Keywords
Cite
@article{arxiv.2308.05923,
title = {Genus one singularities in mean curvature flow},
author = {Adrian Chun-Pong Chu and Ao Sun},
journal= {arXiv preprint arXiv:2308.05923},
year = {2025}
}
Comments
37 pages. Accepted by Geometry & Topology. v3: We added a remark to address the genus one example by Buzano-Nguyen-Schulz and their numerical simulation