| 摘要: |
| 本文旨在研究欧氏平面内初始为星形且中心对称的闭曲线,在一类保长度流作用下的演化问题. 利用保长度流理论,证明了该类曲线的演化具有渐近收敛性,即曲线在任意阶光滑(C∞)意义下,最终会光滑地变形为一个标准圆.该结果推广了保长度流下曲线渐近行为的相关结论, 为理解该类特殊闭曲线在几何流作用下的长期形态提供了更具普适性的理论依据. |
| 关键词: 保长度流 星形曲线 发散型拟线性抛物方程 |
| DOI： |
| 分类号:O186.11 |
| 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). |
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| A CLASS OF LENGTH-PRESERVING PLANAR STAR-SHAPED CENTRALLY SYMMETRIC CLOSED CURVE FLOWS |
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CHENG Qi-yuan, XU Meng-ying, GUO Shun-zi
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School of Mathematics, Yunnan Normal University, Kunming 650500, China
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| 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. |
| Key words: Length-preserving flow Star-shaped curve Divergret quasi-linear parabolic equation |
