On a nonlocal contracting flow for closed convex plane curves

Abstract

The aim of this paper is to present a convex curve evolution problem which is determined by both local (curvature [Formula: see text]) and global (area [Formula: see text]) geometric quantities of the evolving curve. This flow will decrease the perimeter and the area of the evolving curve and make the curve more and more circular during the evolution process. And finally, as [Formula: see text] goes to infinity, the limiting curve will be a finite circle in the [Formula: see text] metric.