数学杂志2026，Vol.46Issue(5)：287-295,9.
一类保长度的平面星形中心对称闭曲线流
A CLASS OF LENGTH-PRESERVING PLANAR STAR-SHAPED CENTRALLY SYMMETRIC CLOSED CURVE FLOWS
摘要
Abstract
This paper aims to investigate the evolution of initially star-shaped,centrally symmetric closed curves in the Euclidean plane under a class of length-preserving flows.Using the theory of length-preserving flows,we prove that the evolution of such curves exhibits asymptotic convergence;specifically,the curves will eventually deform smoothly into a standard circle in the infinitely smooth(C∞)sense.This result generalizes existing findings on the asymptotic behavior of curves under length-preserving flows,providing a more general theoretical foundation for understanding the long-term morphology of these special closed curves under the action of geometric flows.关键词
保长度流/星形曲线/发散型拟线性抛物方程Key words
Length-preserving flow/Star-shaped curve/Divergret quasi-linear parabolic equation分类
数理科学引用本文复制引用
程启媛,胥梦莹,郭顺滋..一类保长度的平面星形中心对称闭曲线流[J].数学杂志,2026,46(5):287-295,9.基金项目
国家自然科学基金资助项目(12261105),云南师范大学2025年度研究生科研创新基金(YJSJJ25-B92). （12261105）
