Deforming Locally Convex Curves into Curves of Constant $k$-order Width
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866929305482690560 |
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| author | Gao, Laiyuan Martini, Horst Zhang, Deyan |
| author_facet | Gao, Laiyuan Martini, Horst Zhang, Deyan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_05267 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Deforming Locally Convex Curves into Curves of Constant $k$-order Width Gao, Laiyuan Martini, Horst Zhang, Deyan Differential Geometry 52A10, 53A04, 53E10, 35K15 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. |
| title | Deforming Locally Convex Curves into Curves of Constant $k$-order Width |
| topic | Differential Geometry 52A10, 53A04, 53E10, 35K15 |
| url | https://arxiv.org/abs/2404.05267 |