We show that the only convex ancient solutions to curve shortening flow are the stationary lines, shrinking circles, Grim Reapers and Angenent ovals, completing the classification initiated by Daskalopoulos, Hamilton and Šešum and X.-J. Wang.

中文翻译：

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凸现曲线缩短流的古老解决方案

我们表明，缩短曲线流动的唯一凸古方法是静止线，收缩圆，死神和椭圆形椭圆，完成了由Daskalopoulos，Hamilton和Šešum和X.-J发起的分类。王