{
  "id": "2012.09490",
  "version": "v1",
  "published": "2020-12-17T10:29:52.000Z",
  "updated": "2020-12-17T10:29:52.000Z",
  "title": "Minimising hulls, p-capacity and isoperimetric inequality on complete Riemannian manifolds",
  "authors": [
    "Mattia Fogagnolo",
    "Lorenzo Mazzieri"
  ],
  "categories": [
    "math.DG",
    "math.AP",
    "math.FA",
    "math.MG"
  ],
  "abstract": "The notion of strictly outward minimising hull is investigated for open sets of finite perimeter sitting inside a complete noncompact Riemannian manifold. Under natural geometric assumptions on the ambient manifold, the strictly outward minimising hull $\\Omega^*$ of a set $\\Omega$ is characterised as a maximal volume solution of the least area problem with obstacle, where the obstacle is the set itself. In the case where $\\Omega$ has $\\mathscr{C}^{1, \\alpha}$-boundary, the area of $\\partial \\Omega^*$ is recovered as the limit of the $p$-capacities of $\\Omega$, as $p \\to 1^+$. Finally, building on the existence of strictly outward minimising exhaustions, a sharp isoperimetric inequality is deduced on complete noncompact manifolds with nonnegative Ricci curvature, provided $3 \\leq n \\leq 7$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-12-17T10:29:52.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "complete riemannian manifolds",
      "strictly outward minimising hull",
      "complete noncompact riemannian manifold",
      "p-capacity",
      "sharp isoperimetric inequality"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}