On an area-preserving inverse curvature flow for plane curves

2025/07/30 by Sun, Zezhen, Wu, Yuting
#35B40 #35K55 #53E99 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2507.22366

Abstract

In this paper, we study a 1/κⁿ-type area-preserving non-local flow of convex closed plane curves for any n>0. We show that the flow exists globally, the length of evolving curve is non-increasing, and the limiting curve will be a circle in the C^∞ metric as time t→∞.

Citations

• A non-local area preserving curve flow
• On a length preserving curve flow
• An isoperimetric inequality with applications to curve shortening

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