A Topological Property of Asymptotically Conical Self-Shrinkers of Small Entropy
A Topological Property of Asymptotically Conical Self-Shrinkers of Small Entropy
复制标题
小熵渐近圆锥自收缩子的拓扑性质
DOI：
10.1215/00127094-3715082
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发表时间：
2015
期刊：
影响因子：
--
通讯作者：
Lu Wang
中科院分区：
文献类型：
--
作者：
J. Bernstein;Lu Wang
对于熵小于或等于圆柱体熵的任意渐近圆锥自收缩体，我们证明了渐近圆锥的连杆必须将单位球精确地分离为两个连通的分量，这两个分量都与自收缩体微分同构。结合Brendle最近的工作，我们得出结论，在所有非平面二维自收缩体中，圆形球体唯一地使熵最小化。这证实了二维的Colding-Ilmanen-Minicozzi-White猜想。
For any asymptotically conical self-shrinker with entropy less than or equal to that of a cylinder we show that the link of the asymptotic cone must separate the unit sphere into exactly two connected components, both diffeomorphic to the self-shrinker. Combining this with recent work of Brendle, we conclude that the round sphere uniquely minimizes the entropy among all non-flat two-dimensional self-shrinkers. This confirms a conjecture of Colding-Ilmanen-Minicozzi-White in dimension two.