On a length-preserving inverse curvature flow of convex closed plane curves

摘要

This paper deals with a 1/kappa(alpha)-type length-preserving nonlocal flow of convex closed plane curves for all alpha > 0. Under this flow, the convexity of the evolving curve is preserved. For a global flow, it is shown that the evolving curve converges smoothly to a circle as t -> infinity. Some numerical blow-up examples and a sufficient condition leading to the global existence of the flow are also constructed. (C) 2020 Elsevier Inc. All rights reserved.