| 摘要: |
| 本文研究了球面曲线在收缩流下的收敛性问题.利用弦弧估计的方法,
获得了球面上具有 $\int_{X} k \, ds = 0$ 的简单闭曲线都可以在流
\[ X_t = \frac{k}{K} N \]
下，最终演化为一条简单闭测地线的结果,推广了球面曲线收敛性猜想的证明方法，丰富曲线流高维研究的几何知识体系. |
| 关键词: 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 |
|
| STUDYING CURVE SHORTENING FLOWS ON THE SPHERE VIA CHORD-ARC ESTIMATES |
|
zhaoyuling
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| Abstract: |
| This paper studies the convergence problem of spherical curves under the contraction flow. By using the chord-arc estimate method, it is obtained that all simple closed curves on the sphere with $\int_{X} k \, ds = 0$ can eventually evolve into a simple closed geodesic under the flow \[ X_t = \frac{k}{K} N. \]This result generalizes the proof method of the convergence conjecture of spherical curves and enriches the geometric knowledge system of high-dimensional research on curve flows. |
| Key words: Chord-arc estimate Curve shortening flow Geodesic Convergence. |
