{
  "id": "1010.4514",
  "version": "v2",
  "published": "2010-10-21T16:21:46.000Z",
  "updated": "2014-01-24T09:51:52.000Z",
  "title": "Existence of Integral $m$-Varifolds minimizing $\\int |A|^p$ and $\\int |H|^p$, $p>m$, in Riemannian Manifolds",
  "authors": [
    "Andrea Mondino"
  ],
  "comment": "33 pages; this second submission corresponds to the published version of the paper, minor typos are fixed",
  "journal": "Calculus of Variations and Partial Differential Equations. January 2014, Volume 49, Issue 1-2, pp 431-470",
  "doi": "10.1007/s00526-012-0588-y",
  "categories": [
    "math.DG"
  ],
  "abstract": "We prove existence and partial regularity of integral rectifiable $m$-dimensional varifolds minimizing functionals of the type $\\int |H|^p$ and $\\int |A|^p$ in a given Riemannian $n$-dimensional manifold $(N,g)$, $2\\leq m<n$ and $p>m$, under suitable assumptions on $N$ (in the end of the paper we give many examples of such ambient manifolds). To this aim we introduce the following new tools: some monotonicity formulas for varifolds in $\\mathbb{R}^S$ involving $\\int |H|^p$, to avoid degeneracy of the minimizer, and a sort of isoperimetric inequality to bound the mass in terms of the mentioned functionals.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-01-24T09:51:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "49Q20",
      "58E99",
      "53A10",
      "49Q05"
    ],
    "keywords": [
      "riemannian manifolds",
      "dimensional varifolds minimizing functionals",
      "dimensional manifold",
      "partial regularity",
      "ambient manifolds"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1010.4514M"
    }
  }
}