No. 2026.04
A Fenchel Theorem for the Gauss maps and uniqueness of minimizers of nonlocal curvature energies
E. Döhrer and A. Dohmen
Subject: Classical analysis and ODEs, differential geometry
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.