整图的二维平均曲率流

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research Pub Date : 2024-10-10 DOI:10.1112/jlms.13000

Andreas Savas Halilaj, Knut Smoczyk

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引用次数: 0

摘要

我们考虑映射 f : R m → R n 的图形平均曲率流 $\mathbf {f}：{\mathbb {R}^{m}}\rightarrow {\mathbb {R}^{n}}$ , m ⩾ 2 $m\geqslant 2$, 并基于适当沉浸子曼形体的新版最大值原理，推导出演化图的增长率估计值，该原理扩展了 Ecker 和 Huisken 在其开创性论文 [Ann.(2) 130:3(1989), 453-471]。在均匀面积递减映射 f : R m → R 2 $\mathbf {f}:{\mathbb {R}^{m}} 的情况下。\rightarrow {\mathbb {R}^{2}}$ , m ⩾ 2 $m\geqslant 2$，我们利用这个最大原则来证明图形性和面积递减属性是保留的。此外，如果初始图形在无穷远处渐近圆锥形，我们证明归一化平均曲率流平滑地收敛于自扩展流。

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Codimension two mean curvature flow of entire graphs

We consider the graphical mean curvature flow of maps $f : R^{m} \to R^{n}$ , $m ⩾ 2$ , and derive estimates on the growth rates of the evolved graphs, based on a new version of the maximum principle for properly immersed submanifolds that extends the well-known maximum principle of Ecker and Huisken derived in their seminal paper [Ann. of Math. (2) 130:3(1989), 453–471]. In the case of uniformly area decreasing maps $f : R^{m} \to R^{2}$ , $m ⩾ 2$ , we use this maximum principle to show that the graphicality and the area decreasing property are preserved. Moreover, if the initial graph is asymptotically conical at infinity, we prove that the normalized mean curvature flow smoothly converges to a self-expander.

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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.

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