{
  "id": "1401.7192",
  "version": "v2",
  "published": "2014-01-28T14:18:00.000Z",
  "updated": "2014-01-30T09:11:06.000Z",
  "title": "Functionals on Closed 2-Surfaces",
  "authors": [
    "Metin Gurses"
  ],
  "comment": "19 pages",
  "categories": [
    "math.DG",
    "hep-th",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We show that the 2-torus in ${\\mathbb R}^3$ is a critical point of a sequence of functionals ${\\cal F}_{n}$ ($n=1,2,3, \\cdots$) defined over compact 2-surfaces in ${\\mathbb R}^3$. When the Lagrange function ${\\cal E}$ is a polynomial of degree $n$ of the mean curvature $H$ of the surface, the radii ($a,r$) of the 2-torus are related as $\\frac{a^2}{r^2}=\\frac{n^2-n}{n^2-n-1}, n \\ge 2$. If the Lagrange function depends on both mean and Gaussian curvatures, the 2- torus remains to be a critical point of ${\\cal F}_{n}$ without any constraints on the radii of the torus.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-01-30T09:11:06.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "functionals",
      "critical point",
      "lagrange function depends",
      "torus remains",
      "mean curvature"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1279032
    }
  }
}