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arXiv · 2604.02042

A Fenchel Theorem for the Gauss maps and uniqueness of minimizers of nonlocal curvature energies

Elias Döhrer·Alexander Dohmen
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Abstract

In this paper, we prove a Fenchel theorem for Gauss maps by providing sharp lower bounds for the path length of Gauss maps of an embedding. By combining the Fenchel-type theorem with various techniques from the field of geometric analysis, we show that circles minimize most generalized tangent-point energies. Furthermore, we prove that disks minimize all fractional Willmore energies among the class of convex planar sets.

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Elias Döhrer, Alexander Dohmen. 2026-04-02. A Fenchel Theorem for the Gauss maps and uniqueness of minimizers of nonlocal curvature energies. https://arxiv.org/abs/2604.02042

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