Convex minimizing curves of the scaling-invariant nonlocal Willmore energy
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914671026503680 |
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| author | Giacomin, Giovanni Schikorra, Armin |
| author_facet | Giacomin, Giovanni Schikorra, Armin |
| contents | We consider the scaling-invariant nonlocal Willmore energy, defined via the nonlocal mean curvature by Caffarelli, Roquejoffre and Savin. Our main result is the existence of minimizers in the class of convex $C^1$-curves. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_05267 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Convex minimizing curves of the scaling-invariant nonlocal Willmore energy Giacomin, Giovanni Schikorra, Armin Analysis of PDEs We consider the scaling-invariant nonlocal Willmore energy, defined via the nonlocal mean curvature by Caffarelli, Roquejoffre and Savin. Our main result is the existence of minimizers in the class of convex $C^1$-curves. |
| title | Convex minimizing curves of the scaling-invariant nonlocal Willmore energy |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2402.05267 |