Classification of noncollapsed translators in $\mathbb{R}^4$

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2021-05-28 DOI:10.4310/cjm.2023.v11.n3.a1

K. Choi, Robert Haslhofer, Or Hershkovits

引用次数: 1

Abstract

In this paper, we classify all noncollapsed singularity models for the mean curvature flow of 3-dimensional hypersurfaces in $\mathbb{R}^4$ or more generally in $4$-manifolds. Specifically, we prove that every noncollapsed translating hypersurface in $\mathbb{R}^4$ is either $\mathbb{R}\times$2d-bowl, or a 3d round bowl, or belongs to the one-parameter family of 3d oval bowls constructed by Hoffman-Ilmanen-Martin-White.

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$\mathbb｛R｝^4中非重叠翻译器的分类$

本文对$\mathbb{R}^4$或更一般地$4$-流形中三维超曲面的平均曲率流的所有非坍缩奇异模型进行了分类。具体来说，我们证明了$\mathbb{R}^4$中的每一个非坍缩平移超曲面要么是$\mathbb{R}\乘以$2d碗，要么是一个3d圆碗，要么属于霍夫曼-伊曼-马丁-怀特构造的三维椭圆碗的单参数族。

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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.