{
  "id": "1503.06674",
  "version": "v2",
  "published": "2015-03-23T15:05:36.000Z",
  "updated": "2015-04-10T02:50:20.000Z",
  "title": "On the shape of compact hypersurfaces with almost constant mean curvature",
  "authors": [
    "Giulio Ciraolo",
    "Francesco Maggi"
  ],
  "comment": "36 pages, 2 figures. In this version we have added an appendix about almost umbilical surfaces",
  "categories": [
    "math.AP",
    "math.DG",
    "math.MG"
  ],
  "abstract": "The distance of an almost constant mean curvature boundary from a finite family of disjoint tangent balls with equal radii is quantitatively controlled in terms of the oscillation of the scalar mean curvature. This result allows one to quantitatively describe the geometry of volume-constrained stationary sets in capillarity problems.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-03-23T15:05:36.000Z",
      "abstract": "We show that the oscillation of the scalar mean curvature of the boundary of a set controls in a quantitative way its distance from a finite family of disjoint tangent balls of equal radii. This result allows one to quantitatively describe the geometry of volume-constrained stationary sets in capillarity problems.",
      "comment": "33 pages, 2 figures",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-04-10T02:50:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "49Q10",
      "49Q20",
      "53A10"
    ],
    "keywords": [
      "constant mean curvature",
      "compact hypersurfaces",
      "scalar mean curvature",
      "disjoint tangent balls",
      "set controls"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 36,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150306674C"
    }
  }
}