{
  "id": "0710.1396",
  "version": "v1",
  "published": "2007-10-07T05:43:37.000Z",
  "updated": "2007-10-07T05:43:37.000Z",
  "title": "The isoperimetric profile of a compact Riemannian Manifold for small volumes",
  "authors": [
    "Stefano Nardulli"
  ],
  "comment": "43 pages",
  "categories": [
    "math.DG"
  ],
  "abstract": "We show that, the solutions of the isoperimetric problem for small volumes are $C^{2,\\alpha}$-close to small spheres. On the way, we define a class of submanifolds called pseudo balls, defined by an equation weaker than constancy of mean curvature. We show that in a neighborhood of each point of a compact riemannian manifold, there is a unique family concentric pseudo balls which contains all the pseudo balls $C^{2,\\alpha}$-close to small spheres. This allows us to reduce the isoperimetric problem for small volumes to a variational problem in finite dimension.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-10-07T05:43:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C21",
      "58J60",
      "58-99",
      "28-99",
      "49-99"
    ],
    "keywords": [
      "compact riemannian manifold",
      "small volumes",
      "isoperimetric profile",
      "isoperimetric problem",
      "unique family concentric pseudo balls"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 43,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0710.1396N"
    }
  }
}