On Ilmanen’s multiplicity-one conjecture for mean curvature flow with type- mean curvature
Haozhao Li
University of Science and Technology of China, Hefei, ChinaBing 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](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserial-issues%2Fcover-jems-volume-24-issue-1.png&w=3840&q=90)
Abstract
In this paper, we show that if the mean curvature of a closed smooth embedded mean curvature flow in is of type-, 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-. As a corollary, we show that the mean curvature at the first singular time of a closed smooth embedded mean curvature flow in is at least of type-.
Cite this article
Haozhao Li, Bing Wang, On Ilmanen’s multiplicity-one conjecture for mean curvature flow with type- mean curvature. J. Eur. Math. Soc. 24 (2022), no. 1, pp. 37–135
DOI 10.4171/JEMS/1090