On A Non-local Curve Flow In The Plane

The aim of this paper is to investigate a evolution problem for convex plane curves.Let X(u,t):[a,b]×[0,∞)→R2 be a family of closcd planer curves with X(u,0)=X0(u)being a closed,strictly convex curve.Consider the following evolution problem: Xt=(?)N A(t)=(?)du X(u,0)=X0(u).This curve evolving problem is a curve shortening evolution problem which will decrease both the perimeter of the evolving curve and the area it bounds and make the evolving curve more and more circular during the evolution process.And finally,as the time t goes to infinity,the limiting curve will be a finite circle in the "C∞" metric.