| 摘要: |
本文研究了如下曲线收缩流：
Xt=k/KN利用球面弦弧估计方法,获得了任意初始光滑嵌入闭球面曲线在该流下演化会保持总测地曲率∫Xkds=0不变,最终收敛为球面上一条简单闭测地线的结果,这为Gage猜想在球面上成立推广了比较简洁的证明. |
| 关键词: 球面弦弧估计 曲线收缩流 测地线 收敛性 |
| DOI： |
| 分类号:O186.1 |
| 基金项目:贵州财经大学研究生科研项目基金资助(2025BAZYSY218),贵州省科技计划项目基金资助(黔科合基础MS(2026)071). |
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| STUDYING A CLASS OF CURVE FLOWS ON THE SPHERE VIA CHORD-ARC ESTIMATES |
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ZHAO Yu-ling
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School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang 550025, China
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| Abstract: |
In this paper, we study the following curve shortening flow:
Xt=k/KN.
Using the spherical chord-arc estimate method, we obtain that any initially smooth embedded closed spherical curve evolving under this flow preserves the vanishing total geodesic curvature ∫Xk, and eventually converges to a simple closed geodesic on the sphere. This provides a relatively concise proof for the extension of Gage’ s conjecture to the sphere. |
| Key words: Chord-arc estimate curve shortening flow geodesic convergence |
