{
  "id": "1301.6322",
  "version": "v1",
  "published": "2013-01-27T06:37:41.000Z",
  "updated": "2013-01-27T06:37:41.000Z",
  "title": "Existence and Regularity for a Curvature Dependent Variational Problem",
  "authors": [
    "Jochen Denzler"
  ],
  "comment": "18 pages, 1 figure",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "It is proved that smooth closed curves of given length minimizing the principal eigenvalue of the Schr\\\"odinger operator $-\\frac{d^2}{ds^2}+\\kappa^2$ exist. Here $s$ denotes the arclength and $\\kappa$ the curvature. These minimizers are automatically planar, analytic, convex curves. The straight segment, traversed back and forth, is the only possible exception that becomes admissible in a more generalized setting. In proving this, we overcome the difficulty from a lack of coercivity and compactness by a combination of methods.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-01-27T06:37:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53A04",
      "49J45",
      "49N60",
      "49R50"
    ],
    "keywords": [
      "curvature dependent variational problem",
      "regularity",
      "principal eigenvalue",
      "smooth closed curves",
      "convex curves"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1301.6322D"
    }
  }
}