浸没网络的各向异性曲率流

IF 1.2 3区数学 Q1 MATHEMATICS

Milan Journal of Mathematics Pub Date : 2021-05-07 DOI:10.1007/s00032-021-00329-8

Heiko Kröner, Matteo Novaga, Paola Pozzi

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引用次数: 3

摘要

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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Anisotropic Curvature Flow of Immersed Networks

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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来源期刊

Milan Journal of Mathematics 数学-数学

CiteScore

2.60

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Milan Journal of Mathematics (MJM) publishes high quality articles from all areas of Mathematics and the Mathematical Sciences. The authors are invited to submit "articles with background", presenting a problem of current research with its history and its developments, the current state and possible future directions. The presentation should render the article of interest to a wider audience than just specialists. Many of the articles will be "invited contributions" from speakers in the "Seminario Matematico e Fisico di Milano". However, also other authors are welcome to submit articles which are in line with the "Aims and Scope" of the journal.