一类收缩到一点的非局部平面凸曲线流

A Kind of Nonlocal Plane Convex Curves of Contraction to a Point

研究了一类含参数的非局部平面凸曲线流,应用偏微分方程的极大值原理和先验估计,证明了发展曲线在演化过程中保持凸性,曲线的周长和面积均单调递减,曲线越变越圆且在有限时间内收缩于一点.

In this paper,a kind of nonlocal plane convex curve flow has been discussed.From the maximum principle and a priori estimates of partial differential equations,it is proved that the convex curve preserves convexity,the perimeter of the evolving curve and the area it bounds decrease monotonically,and the convex curve becomes more and more circular and shrinks to a point in finite time.