Continuous dependence of curvature flow on initial conditions

IF 0.5 3区数学 Q3 MATHEMATICS

Journal of Topology and Analysis Pub Date : 2023-11-10 DOI:10.1142/s1793525323500371

Michael Gene Dobbins

引用次数: 1

Abstract

We study the evolution of a Jordan curve on the 2-sphere by curvature flow, also known as curve shortening flow, and by level-set flow, which is a weak formulation of curvature flow. We show that the evolution of the curve depends continuously on the initial curve in Frechet distance in the case where the curve bisects the sphere. This even holds in the limit as time goes to infinity. This builds on Joseph Lauer's work on existence and uniqueness of solutions to the curvature flow problem on the sphere when the initial curve is not smooth.

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曲率流动对初始条件的连续依赖性

本文研究了曲率流(也称为曲线缩短流)和水平集流(曲率流的一种弱表述)在2球上Jordan曲线的演化。我们证明了当曲线与球体平分时，曲线的演化连续依赖于Frechet距离内的初始曲线。这甚至在时间趋于无穷时也成立。这建立在Joseph Lauer关于初始曲线不光滑时球面上曲率流动问题解的存在性和唯一性的基础上。

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

Journal of Topology and Analysis MATHEMATICS-

CiteScore

1.50

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： This journal is devoted to topology and analysis, broadly defined to include, for instance, differential geometry, geometric topology, geometric analysis, geometric group theory, index theory, noncommutative geometry, and aspects of probability on discrete structures, and geometry of Banach spaces. We welcome all excellent papers that have a geometric and/or analytic flavor that fosters the interactions between these fields. Papers published in this journal should break new ground or represent definitive progress on problems of current interest. On rare occasion, we will also accept survey papers.