曲线缩短流对平移孤子的收敛性

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2021-07-10 DOI:10.1353/ajm.2021.0027

Beomjun Choi, K. Choi, P. Daskalopoulos

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引用次数: 2

摘要

研究了嵌入在$\Bbb{R}^2$中的完全非紧凸曲线在$\alpha$-曲线缩短流下对于指数$\alpha>{1\ / 2}$的渐近行为。我们证明了任何这样的曲线在$\ α $-曲线缩短流下收敛到唯一的平移孤子，其两端渐近于同一平行线。即使在标准情况$\alpha=1$下，这也是一个新的结果，并且我们证明了所有指数直到临界情况$\alpha>{1\ / 2}$。

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Convergence of curve shortening flow to translating soliton

abstract:This paper concerns with the asymptotic behavior of complete non-compact convex curves embedded in $\Bbb{R}^2$ under the $\alpha$-curve shortening flow for exponents $\alpha>{1\over 2}$. We show that any such curve having in addition its two ends asymptotic to two parallel lines, converges under $\alpha$-curve shortening flow to the unique translating soliton whose ends are asymptotic to the same parallel lines. This is a new result even in the standard case $\alpha=1$, and we prove for all exponents up to the critical case $\alpha>{1\over 2}$.

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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.