{
  "id": "math/0702237",
  "version": "v1",
  "published": "2007-02-08T23:58:54.000Z",
  "updated": "2007-02-08T23:58:54.000Z",
  "title": "Variation of Perimeter Measure in sub-Riemannian geometry",
  "authors": [
    "Robert K. Hladky",
    "Scott D. Pauls"
  ],
  "comment": "37 pages",
  "categories": [
    "math.DG"
  ],
  "abstract": "We derive a formula for the first variation of horizontal perimeter measure for $C^2$ hypersurfaces of completely general sub-Riemannian manifolds, allowing for the existence of characteristic points. For $C^2$ hypersurfaces in vertically rigid sub-Riemannian manifolds we also produce a second variation formula for variations supported away from the characteristic locus. This variation formula is used to show the bubble sets in \\hn{2} are stable under volume preserving variations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-02-08T23:58:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C17",
      "53C42"
    ],
    "keywords": [
      "sub-riemannian geometry",
      "horizontal perimeter measure",
      "vertically rigid sub-riemannian manifolds",
      "second variation formula",
      "general sub-riemannian manifolds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 37,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007math......2237H"
    }
  }
}