Convex minimizing curves of the scaling-invariant nonlocal Willmore energy

Giovanni Giacomin; Armin Schikorra

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arXiv · 2402.05267

Convex minimizing curves of the scaling-invariant nonlocal Willmore energy

Giovanni Giacomin·Armin Schikorra

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Abstract

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.

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Giovanni Giacomin, Armin Schikorra. 2024-02-07. Convex minimizing curves of the scaling-invariant nonlocal Willmore energy. https://arxiv.org/abs/2402.05267

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