Communications in Analysis and Geometry

Volume 29 (2021)

Number 5

A $\operatorname{log}$-type non-local flow of convex curves

Pages: 1157 – 1182

DOI: https://dx.doi.org/10.4310/CAG.2021.v29.n5.a5

Authors

Laiyuan Gao (School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou City, Jiangsu Province, China)

Shengliang Pan (School of Mathematical Sciences, Tongji University, Shanghai, China)

Ke Shi (School of Mathematical Sciences, Tongji University, Shanghai, China)

Abstract

In this paper, a $\operatorname{log}$-type non-local flow of closed convex plane curves is studied. This flow decreases the perimeter of the evolving curve, increases the area it bounds and deforms it into a finite circle as time goes to infinity.

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The first author is supported by the National Natural Science Foundation of China (No.11801230) and the Science Foundation of Jiangsu Normal University under Grant 16XLR034.

The second and third authors are supported by the Science Research Project of Shanghai (No.16ZR1439200) and the National Natural Science Foundation of China (No.11671298 and No.12071347).

Received 28 May 2018

Accepted 2 January 2019

Published 1 December 2021