Deforming Locally Convex Curves into Curves of Constant k-order Width

2024/04/08 by Laiyuan Gao, Gao, Laiyuan, Horst Martini +3
Computer Science · #35K15 #52A10 #53A04 #53E10 #Advanced Graph Theory Research #Cellular Automata and Applications #Computational Geometry and Mesh Generation #Differential Geometry (math.DG) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2404.05267

openalex publication_date 2024/04/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A nonlocal curvature flow is introduced to evolve locally convex curves in the plane. It is proved that this flow with any initial locally convex curve has a global solution, keeping the local convexity and the elastic energy of the evolving curve, and that, as the time goes to infinity, the curve converges to a smooth, locally convex curve of constant k-order width. In particular, the limiting curve is a multiple circle if and only if the initial locally convex curve is k-symmetric.

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