Deforming locally convex curves into curves of constant k-order width

IF 0.6 4区数学 Q3 MATHEMATICS Differential Geometry and its Applications Pub Date : 2024-10-22 DOI:10.1016/j.difgeo.2024.102192

引用次数: 0

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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将局部凸曲线变形为 k 阶宽度不变的曲线

引入了一种非局部曲率流来演化平面中的局部凸曲线。研究证明，任何初始局部凸曲线的非局部曲率流都有一个全局解，它保持了演化曲线的局部凸性和弹性能量，而且随着时间的无穷大，曲线会收敛到一条具有恒定 k 阶宽度的光滑局部凸曲线。特别是，当且仅当初始局部凸曲线是 k 对称曲线时，极限曲线是一个多重圆。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Differential Geometry and its Applications 数学-数学

CiteScore

1.00

自引率

20.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Differential Geometry and its Applications publishes original research papers and survey papers in differential geometry and in all interdisciplinary areas in mathematics which use differential geometric methods and investigate geometrical structures. The following main areas are covered: differential equations on manifolds, global analysis, Lie groups, local and global differential geometry, the calculus of variations on manifolds, topology of manifolds, and mathematical physics.

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