Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2506.20142 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915358246436864 |
|---|---|
| author | Heller, Lynn Heller, Sebastian Traizet, Martin |
| author_facet | Heller, Lynn Heller, Sebastian Traizet, Martin |
| contents | Building on Hitchin's work of the Wess-Zumino-Witten term for harmonic maps into Lie groups, we derive a formula for the enclosed volume of a compact CMC surface $f$ in $\mathbb S^3$ in terms of a holonomy on the Chern-Simons bundle and the Willmore functional. By construction the enclosed volume only depends on the gauge classes of the associated family of flat connections of $f$. In this paper we show in various examples the effectiveness of this formula, in particular for surfaces of genus $g\geq2.$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_20142 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Application of Chern-Simons gauge theory to the enclosed volume of constant mean curvature surfaces in the 3-sphere Heller, Lynn Heller, Sebastian Traizet, Martin Differential Geometry Mathematical Physics Building on Hitchin's work of the Wess-Zumino-Witten term for harmonic maps into Lie groups, we derive a formula for the enclosed volume of a compact CMC surface $f$ in $\mathbb S^3$ in terms of a holonomy on the Chern-Simons bundle and the Willmore functional. By construction the enclosed volume only depends on the gauge classes of the associated family of flat connections of $f$. In this paper we show in various examples the effectiveness of this formula, in particular for surfaces of genus $g\geq2.$ |
| title | Application of Chern-Simons gauge theory to the enclosed volume of constant mean curvature surfaces in the 3-sphere |
| topic | Differential Geometry Mathematical Physics |
| url | https://arxiv.org/abs/2506.20142 |