{
  "id": "2506.20142",
  "version": "v1",
  "published": "2025-06-25T05:30:19.000Z",
  "updated": "2025-06-25T05:30:19.000Z",
  "title": "Application of Chern-Simons gauge theory to the enclosed volume of constant mean curvature surfaces in the 3-sphere",
  "authors": [
    "Lynn Heller",
    "Sebastian Heller",
    "Martin Traizet"
  ],
  "categories": [
    "math.DG",
    "math-ph",
    "math.MP"
  ],
  "abstract": "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 $g\\geq2.$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-06-25T05:30:19.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "constant mean curvature surfaces",
      "chern-simons gauge theory",
      "enclosed volume",
      "application",
      "compact cmc surface"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}