The evolution of area-preserving and length-preserving inverse curvature flows for immersed locally convex closed plane curves

In this paper, we study an area-preserving inverse curvature flow and a length-preserving inverse curvature flow for immersed locally convex closed plane curves with rotation number m is an element of N+. The global-in-time flows are shown to converge smoothly to m-fold round circles as time goes to infinity. The sufficient conditions on initial curve are also found to guarantee the occurrence of the flow's singularity at finite time.(c) 2022 Elsevier Inc. All rights reserved.