曲线缩短流对平移孤子的收敛性

IF 1.7 1区数学 Q1 MATHEMATICS

American Journal of Mathematics 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

American Journal of Mathematics 数学-数学

CiteScore

3.20

自引率

0.00%

发文量

审稿时长

24 months

期刊介绍： The oldest mathematics journal in the Western Hemisphere in continuous publication, the American Journal of Mathematics ranks as one of the most respected and celebrated journals in its field. Published since 1878, the Journal has earned its reputation by presenting pioneering mathematical papers. It does not specialize, but instead publishes articles of broad appeal covering the major areas of contemporary mathematics. The American Journal of Mathematics is used as a basic reference work in academic libraries, both in the United States and abroad.