On a non-local perimeter-preserving curve evolution problem for convex plane curves

This paper deals with a non-local evolution problem for closed convex plane curves which preserves the perimeter of the evolving curve but enlarges the area it bounds and makes the evolving curve more and more circular during the evolution process. And the final shape of the evolving curve will be a circle in the C ^∞ metric as the time t goes to infinity. The first author is supported in part by the National Science Foundation of China (No.10671066) and the Shanghai Leading Academic Discipline Project (No. B407).