平面中一族光滑凸曲线流

A Family of Smooth Convex Curve Flows in the Plane

本文定义了平面中的一族曲线流,当初始曲线为封闭的凸曲线时,证明了在演化过程中,当曲线的长度减小时,所围成的封闭图形的面积增加;并证明了该曲线流的解始终存在,且当t→+∞ 时,曲线按C0范数收敛到有限圆.

A family of curve flows in the plane is defined in this paper.It is testified that the length of the curve decreases in the course of evolution when the initial curve is the enclosed convex curve,while the area of the enclosed graph increases.It is also proved that the solution of the very curve flow exists all the time.The curve converges to a limited circle in C0 norm when t→+∞。