{
  "id": "2109.07057",
  "version": "v1",
  "published": "2021-09-15T02:52:41.000Z",
  "updated": "2021-09-15T02:52:41.000Z",
  "title": "Equivalences among parabolicity, comparison principle and capacity on complete Riemannian manifolds",
  "authors": [
    "A. Aiolfi",
    "L. Bonorino",
    "J. Ripoll",
    "M. Soret",
    "M. Ville"
  ],
  "categories": [
    "math.DG",
    "math.AP"
  ],
  "abstract": "In this work we establish new equivalences for the concept of $p$-parabolic Riemannian manifolds. We define a concept of comparison principle for elliptic PDE's on exterior domains of a complete Riemannian manifold $M$ and prove that $M$ is $p$-parabolic if and only if this comparison principle holds for the $p$-Laplace equation. We show also that the $p$-parabolicity of $M$ implies the validity of this principle for more general elliptic PDS's and, in some cases, these results can be extended for non $p$-parabolic manifolds or unbounded solutions, provided that some growth of these solutions are assumed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-09-15T02:52:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J93",
      "58J05",
      "58J32"
    ],
    "keywords": [
      "complete riemannian manifold",
      "parabolicity",
      "equivalences",
      "comparison principle holds",
      "parabolic riemannian manifolds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}