{
  "id": "math/0609325",
  "version": "v2",
  "published": "2006-09-12T07:20:49.000Z",
  "updated": "2006-10-19T11:22:44.000Z",
  "title": "Surfaces of revolution in the Heisenberg group and the spectral generalization of the Willmore functional",
  "authors": [
    "Dmitry A. Berdinsky",
    "Iskander A. Taimanov"
  ],
  "comment": "21 pages, some typos and references corrected",
  "journal": "Siberian Math. J. 48:3 (2007), 395-407",
  "categories": [
    "math.DG"
  ],
  "abstract": "We study the generalization of the Willmore functional for surfaces in the three-Heisenberg group. Its construction is based on the spectral theory of the Dirac operator coming to the Weierstrass representation of surfaces (see math.DG/0503707). By using surfaces of revolution we demonstrate that it resembles the Willmore functional for surfaces in the Euclidean space in many geometrical respects. We also observe the relation of these functionals to the isoperimetric problem.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2006-10-19T11:22:44.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "willmore functional",
      "spectral generalization",
      "revolution",
      "isoperimetric problem",
      "euclidean space"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......9325B"
    }
  }
}