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arXiv · 2409.01463

Revisiting generic mean curvature flow in $\mathbb{R}^3$

Otis Chodosh·Kyeongsu Choi·Christos Mantoulidis·Felix Schulze
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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.

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Otis Chodosh, Kyeongsu Choi, Christos Mantoulidis, Felix Schulze. 2024-09-02. Revisiting generic mean curvature flow in $\mathbb{R}^3$. https://doi.org/10.1515/crelle-2025-0064

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