Anisotropic Curvature Flow of Immersed Networks

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2021-05-07 DOI:10.1007/s00032-021-00329-8

Heiko Kröner, Matteo Novaga, Paola Pozzi

引用次数: 3

Abstract

We consider motion by anisotropic curvature of a network of three curves immersed in the plane meeting at a triple junction and with the other ends fixed. We show existence, uniqueness and regularity of a maximal geometric solution and we prove that, if the maximal time is finite, then either the length of one of the curves goes to zero or the \(L^2\)-norm of the anisotropic curvature blows up.

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浸没网络的各向异性曲率流

我们考虑一个由三条曲线组成的网络的各向异性曲率的运动，这三条曲线在平面上以三结点相交，另一端固定。证明了极大几何解的存在性、唯一性和正则性，并证明了如果极大时间是有限的，则要么其中一条曲线的长度趋近于零，要么各向异性曲率的\(L^2\)范数爆发。

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.