AI 中文总结
针对Grayson与Gage提出的闭曲面上不朽曲线缩短流的极限测地线是否唯一的问题，在球面$\rm S^2$上构造反例，证明该极限测地线不唯一，否定回答了该问题。
AI 中文摘要
Grayson和Gayson证明了闭曲面上简单闭曲线的不朽曲线缩短流会依子序列收敛到一条闭测地线，并提出该极限测地线是否唯一的问题。我们通过在球面$\boldsymbol{\rm S}^2$上构造一个光滑黎曼度量，以及一个不朽的简单闭曲线缩短流，沿不同时间序列收敛到一个单参数族中每条不同的简单闭测地线，从而否定地回答了这个问题。
英文摘要
Grayson and Gage proved that an immortal curve shortening flow of simple closed curves on a closed surface converges subsequentially to a closed geodesic, and they asked whether this limiting geodesic is unique. We answer this question negatively by constructing a smooth Riemannian metric on $\mathbb{S}^2$ and an immortal simple closed curve shortening flow that converges along different sequences of times to every geodesic in a one-parameter family of distinct simple closed geodesics.
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