On bounds of entropy and total curvature for ancient curve shortening flows

IF 0.7 3区数学 Q3 MATHEMATICS

Annals of Global Analysis and Geometry Pub Date : 2025-10-06 DOI:10.1007/s10455-025-10019-y

Wei-Bo Su, Kai-Wei Zhao

引用次数: 0

Abstract

Bounds of total curvature and entropy are two common conditions placed on mean curvature flows. We show that these two hypotheses are equivalent for the class of ancient complete embedded smooth planar curve shortening flows, which are one-dimensional mean curvature flows. As an application, we give a short proof of the uniqueness and classification of tangent flow at infinity of an ancient smooth complete non-compact curve shortening flow with finite entropy embedded in \(\mathbb {R}^2\).

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古弯曲缩短流的熵和总曲率边界

总曲率和熵的边界是平均曲率流的两个常见条件。我们证明了这两个假设对于一类古老的完全嵌入光滑平面曲线缩短流是等价的，这类流是一维平均曲率流。作为应用，我们给出了一个包含有限熵的古老光滑完全非紧曲线缩短流的无穷远处切线流的唯一性和分类的简短证明 \(\mathbb {R}^2\)．

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

Annals of Global Analysis and Geometry 数学-数学

CiteScore

1.20

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： This journal examines global problems of geometry and analysis as well as the interactions between these fields and their application to problems of theoretical physics. It contributes to an enlargement of the international exchange of research results in the field. The areas covered in Annals of Global Analysis and Geometry include: global analysis, differential geometry, complex manifolds and related results from complex analysis and algebraic geometry, Lie groups, Lie transformation groups and harmonic analysis, variational calculus, applications of differential geometry and global analysis to problems of theoretical physics.