一种保持修正弹性能量的非局部曲线流  

On a Non-local Curve Flow with Fixed Modified Elastic Energy

作　　者：孙泽镇 Zezhen Sun(The Department of General Education,Anhui Water Conservancy Technical College,Hefei 231603,P.R.China;School of Mathematical Sciences,East China Normal University,Shanghai 200241,P.R.China)

机构地区：[1]安徽水利水电职业技术学院基础教学部,合肥231603 [2]华东师范大学数学科学学院,上海200241

出　　处：《数学学报(中文版)》2025年第2期278-289,共12页Acta Mathematica Sinica:Chinese Series

基　　金：上海市科学技术委员会(22DZ2229014);上海PMMP重点实验室(18DZ2271000)。

摘　　要：本文研究一种非局部曲线流,它会保持演化曲线的凸性和修正的弹性能量∫_(0)^(l)κ^(2)ds-∈L(∈≥0)不变.我们将证明这个流会整体存在,且演化曲线的长度递减,最终随着时间趋向无穷时,其在C^(∞)度量下会收敛到一个有限圆.作为这个流的应用,我们将证明两个新的几何不等式.This paper deals with a non-local curvature flow which preserves convexity and the modified elastic energy ∫_(0)^(l)κ^(2)ds-∈L(∈≥0)of the evolving curve.We show that the flow exists globally,the length of the evolving curve is non-increasing,and the evolving curve converges to a finite circle in C^(∞) topology as time goes to infinity.As an application of this flow,we prove two new geometric inequalities.

关 键 词：闭凸平面曲线 修正弹性能量 存在性 收敛性 

分 类 号：O186.1[理学—数学]