非局部平面曲线流

Nonlocal plane curve ows

本文首先综述近年来关于平面曲线流(尤其是非局部平面凸曲线流)的一系列研究进展.之后研究平面凸曲线的一个广义保面积流,并证明在演化过程中,演化曲线始终保持凸性,并且长度递减,最终当时间趋于无穷时,演化曲线光滑收敛到一个圆周.

In this paper,we rst survey some progress of plane curve ows(especially nonlocal convex curve ows)in recent years.Then we study a generalized area-preserving ow of convex curves.We prove that this ow keeps the convexity of the evolving curve and decreases its perimeter during the evolution process.Finally,as time goes to in nity,the evolving curve will converge smoothly to a circle.