平面中一种保长度的曲线流

On a Type of Perimeter-preserving Curve Flow in Plane

本文定义了平面中的一种曲线流,当初始曲线为封闭的凸曲线时,证明了曲线的长度保持不变,同时所围图形的面积增加,并且,曲线流的解对t?[0,(10)?)都存在,当t?(10)?时,曲线按0C范数收敛到圆.

A type of curve flow in the plane is defined in this paper.It turns out that the length of the curve is remained unchanged when the initial curve is a closed convex curve.Meanwhile,the area of the surrounded graphic increases and the solution of the curve flow exists towards t∈[0,+∞).When t→+∞,the curve converges to a circle is based on the C^0 norm.