Revisiting generic mean curvature flow in ℝ³

2024/09/02 by Chodosh, Otis, Choi, Kyeongsu, Mantoulidis, Christos +1 · 1 citation
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2409.01463

Abstract

Bamler--Kleiner recently proved a multiplicity-one theorem for mean curvature flow in R³ 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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• Mean curvature flow through singularities

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