A Fenchel Theorem for the Gauss maps and uniqueness of minimizers of nonlocal curvature energies
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915909531074560 |
|---|---|
| author | Döhrer, Elias Dohmen, Alexander |
| author_facet | Döhrer, Elias Dohmen, Alexander |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_02042 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Fenchel Theorem for the Gauss maps and uniqueness of minimizers of nonlocal curvature energies Döhrer, Elias Dohmen, Alexander Classical Analysis and ODEs Differential Geometry 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. |
| title | A Fenchel Theorem for the Gauss maps and uniqueness of minimizers of nonlocal curvature energies |
| topic | Classical Analysis and ODEs Differential Geometry |
| url | https://arxiv.org/abs/2604.02042 |