On Ilmanen's multiplicity-one conjecture for mean curvature flow with type-I mean curvature

Haozhao Li; Bing Wang

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arXiv · 1811.08654

On Ilmanen's multiplicity-one conjecture for mean curvature flow with type-I mean curvature

Haozhao Li·Bing Wang

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Abstract

In this paper, we show that if the mean curvature of a closed smooth embedded mean curvature flow in R^3 is of type-I, then the rescaled flow at the first finite singular time converges smoothly to a self-shrinker flow with multiplicity one. This result confirms Ilmanen's multiplicity-one conjecture under the assumption that the mean curvature is of type-I. As a corollary, we show that the mean curvature at the first singular time of a closed smooth embedded mean curvature flow in R^3 is at least of type-I.

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Haozhao Li, Bing Wang. 2018-11-21. On Ilmanen's multiplicity-one conjecture for mean curvature flow with type-I mean curvature. https://arxiv.org/abs/1811.08654

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