On Ilmanen’s multiplicity-one conjecture for mean curvature flow with type-$I$ mean curvature
On Ilmanen’s multiplicity-one conjecture for mean curvature flow with type-$I$ mean curvature
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DOI：
10.4171/jems/1090
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发表时间：
2018-11
期刊：
影响因子：
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通讯作者：
Haozhao Li;B. Wang
中科院分区：
文献类型：
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作者：
Haozhao Li;B. Wang
本文证明了如果R^3中的闭光滑嵌入平均曲率流的平均曲率为I型，则重标流在第一个有限奇异时刻光滑收敛到重数为1的自收缩流.这一结果证实了Ilmanen在平均曲率为I型的假设下的重一猜想。作为推论，我们证明了R^3中闭光滑嵌入平均曲率流在第一奇异时刻的平均曲率至少是I型的。
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.