Translating annuli for mean curvature flow

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-08-13 DOI:10.1016/j.aim.2024.109875

David Hoffman , Francisco Martín , Brian White

{"title":"Translating annuli for mean curvature flow","authors":"David Hoffman , Francisco Martín , Brian White","doi":"10.1016/j.aim.2024.109875","DOIUrl":null,"url":null,"abstract":"<div>We construct a family <math><mi>A</mi></math> of complete, properly embedded, annular translators M such that M lies in a slab and is invariant under reflections in the vertical coordinate planes. For each M in <math><mi>A</mi></math>, M is asymptotic as <math><mi>z</mi><mo>→</mo><mo>−</mo><mo>∞</mo></math> to four vertical planes <math><mo>{</mo><mi>y</mi><mo>=</mo><mo>±</mo><mi>b</mi><mo>}</mo></math> and <math><mo>{</mo><mi>y</mi><mo>=</mo><mo>±</mo><mi>B</mi><mo>}</mo></math> where <math><mn>0</mn><mo><</mo><mi>b</mi><mo>≤</mo><mi>B</mi><mo><</mo><mo>∞</mo></math>. We call b and B the inner width and the (outer) width of M. We show that for each <math><mi>b</mi><mo>≥</mo><mi>π</mi><mo>/</mo><mn>2</mn></math> and each <math><mi>s</mi><mo>></mo><mn>0</mn></math>, there is an <math><mi>M</mi><mo>∈</mo><mi>A</mi></math> with inner width b and with necksize s. (We also show that there are no translators with inner width <math><mo><</mo><mi>π</mi><mo>/</mo><mn>2</mn></math> having the properties of the examples we construct.)</div>","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2024-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0001870824003906","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}

引用次数: 0

Abstract

We construct a family $A$ of complete, properly embedded, annular translators M such that M lies in a slab and is invariant under reflections in the vertical coordinate planes. For each M in $A$ , M is asymptotic as $z \to - \infty$ to four vertical planes ${y = \pm b}$ and ${y = \pm B}$ where $0 0$ , there is an $M \in A$ with inner width b and with necksize s. (We also show that there are no translators with inner width $< π / 2$ having the properties of the examples we construct.)

查看原文本刊更多论文

平均曲率流的平移环面

我们构建了一个由完整的、适当嵌入的环形平移器 M 组成的族 A，使得 M 位于板坯中，并且在垂直坐标平面的反射下保持不变。对于 A 中的每个 M，M 在 z→-∞ 时渐近于四个垂直平面 {y=±b} 和 {y=±B} ，其中 0<b≤B<∞。我们称 b 和 B 为 M 的内宽和（外）宽。我们将证明，对于每个 b≥π/2 和每个 s>0，都存在一个内宽为 b、颈长为 s 的 M∈A（我们还将证明，不存在内宽为 <π/2 的平移器，其性质与我们构建的示例相同）。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

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.