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arXiv · 2404.05267

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

Laiyuan Gao·Horst Martini·Deyan Zhang
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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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Laiyuan Gao, Horst Martini, Deyan Zhang. 2024-04-08. Deforming Locally Convex Curves into Curves of Constant $k$-order Width. https://arxiv.org/abs/2404.05267

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