JournalsjemsVol. 24, No. 1pp. 37–135

On Ilmanen’s multiplicity-one conjecture for mean curvature flow with type-II mean curvature

  • Haozhao Li

    University of Science and Technology of China, Hefei, China
  • Bing Wang

    University of Science and Technology of China, Hefei, China
On Ilmanen’s multiplicity-one conjecture for mean curvature flow with type-$I$ mean curvature cover
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Abstract

In this paper, we show that if the mean curvature of a closed smooth embedded mean curvature flow in R3{\mathbb R}^3 is of type-II, 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-II. As a corollary, we show that the mean curvature at the first singular time of a closed smooth embedded mean curvature flow in R3{\mathbb R}^3 is at least of type-II.

Cite this article

Haozhao Li, Bing Wang, On Ilmanen’s multiplicity-one conjecture for mean curvature flow with type-II mean curvature. J. Eur. Math. Soc. 24 (2022), no. 1, pp. 37–135

DOI 10.4171/JEMS/1090