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On a nonlocal contracting flow for closed convex plane curves

Ruixia Hao

School of Mathematical Sciences, Tongji University, Shanghai 200092, P. R. China

E-mail Address: 1710856@tongji.edu.cn

Corresponding author.

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and

Run Zhang

HuaiBei Experimental High School, HuaiBei 235000, P. R. China

E-mail Address: 364055612@qq.com

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https://doi.org/10.1142/S0129167X23500180Cited by:0 (Source: Crossref)

Abstract

The aim of this paper is to present a convex curve evolution problem which is determined by both local (curvature $κ$ ) and global (area $A$ ) geometric quantities of the evolving curve. This flow will decrease the perimeter and the area of the evolving curve and make the curve more and more circular during the evolution process. And finally, as $t$ goes to infinity, the limiting curve will be a finite circle in the $C^{\infty}$ metric.

This work is supported by the National Science Foundation of China (No. 12071347).

Communicated by Xiaonan Ma

Keywords:

AMSC: 35K15, 35K55, 53A04

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