Mean curvature flow with generic initial data

IF 2.6 1区 数学 Q1 MATHEMATICS
Otis Chodosh, Kyeongsu Choi, Christos Mantoulidis, Felix Schulze
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引用次数: 0

Abstract

We show that the mean curvature flow of generic closed surfaces in \(\mathbb{R}^{3}\) avoids asymptotically conical and non-spherical compact singularities. We also show that the mean curvature flow of generic closed low-entropy hypersurfaces in \(\mathbb{R}^{4}\) is smooth until it disappears in a round point. The main technical ingredient is a long-time existence and uniqueness result for ancient mean curvature flows that lie on one side of asymptotically conical or compact shrinking solitons.

Abstract Image

具有一般初始数据的平均曲率流
我们证明了在\(\mathbb{R}^{3}\)中一般封闭曲面的平均曲率流避免了渐近圆锥和非球形紧凑奇点。我们还证明了在\(\mathbb{R}^{4}\)中一般封闭低熵超曲面的平均曲率流是平滑的,直到它在一个圆点上消失。主要的技术成分是位于渐近圆锥或紧凑收缩孤子一侧的古平均曲率流的长期存在性和唯一性结果。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Inventiones mathematicae
Inventiones mathematicae 数学-数学
CiteScore
5.60
自引率
3.20%
发文量
76
审稿时长
12 months
期刊介绍: This journal is published at frequent intervals to bring out new contributions to mathematics. It is a policy of the journal to publish papers within four months of acceptance. Once a paper is accepted it goes immediately into production and no changes can be made by the author(s).
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