On an area-preserving inverse curvature flow of convex closed plane curves

摘要

This paper deals with the 1/k(alpha)-type area-preserving nonlocal flow of smooth convex closed plane curves for all constant alpha > 0. Under this flow, the convexity of the evolving curve is preserved. Due to the existence of finite time curvature blow-up examples, it is shown that, if the curvature k will not blow up in finite time, the evolving curve will converge smoothly to a circle as t -> infinity. (C) 2021 Elsevier Inc. All rights reserved.