镰刀型曲线的显式表达式——作为曲线收缩流解

Explicit Expression of the Sickle Curve——As a Solution to the Curve Shortening Flow

首先介绍了曲线收缩流的两类特殊的解,然后给出了镰刀型曲线的显式表达且证明了其是曲线收缩流的解,最后利用Frenet标架再次证明了镰刀型曲线是曲线收缩流的显式解.

In this paper,we firstly introduced two kinds of special solutions to the curve shortening flow,then gave an explicit expression of the sickle curve before proving it to be the solution of the curve shortening flow,and lastly proved again that the sickle curve is the explicit solution by using the Frenet fream.