Revisiting generic mean curvature flow in $\mathbb{R}^3$
Differential Geometry
2025-10-09 v3
Abstract
Bamler--Kleiner recently proved a multiplicity-one theorem for mean curvature flow in R^3 and combined it with the authors' work on generic mean curvature flows to fully resolve Huisken's genericity conjecture. In this paper we show that a short density-drop theorem plus the Bamler--Kleiner multiplicity-one theorem for tangent flows at the first nongeneric singular time suffice to resolve Huisken's conjecture -- without relying on the strict genus drop theorem for one-sided ancient flows previously established by the authors.
Keywords
Cite
@article{arxiv.2409.01463,
title = {Revisiting generic mean curvature flow in $\mathbb{R}^3$},
author = {Otis Chodosh and Kyeongsu Choi and Christos Mantoulidis and Felix Schulze},
journal= {arXiv preprint arXiv:2409.01463},
year = {2025}
}
Comments
Final version. To appear in a special bicentennial issue of J. Reine Angew. Math. (Crelle)