{
  "id": "1211.2899",
  "version": "v3",
  "published": "2012-11-13T06:41:35.000Z",
  "updated": "2016-02-23T03:04:03.000Z",
  "title": "Liouville properties for p-harmonic maps with finite q-energy",
  "authors": [
    "Shu-Cheng Chang",
    "Jui-Tang Chen",
    "Shihshu Walter Wei"
  ],
  "comment": "This paper will appear in Transactions of the American Mathematical Society, 2016",
  "categories": [
    "math.DG"
  ],
  "abstract": "We introduce and study an approximate solution of the p-Laplace equation, and a linearlization $L_{\\epsilon}$ of a perturbed p-Laplace operator. By deriving an $L_{\\epsilon}$-type Bochner's formula and a Kato type inequality, we prove a Liouville type theorem for weakly p-harmonic functions with finite p-energy on a complete noncompact manifold M which supports a weighted Poincar\\'{e} inequality and satisfies a curvature assumption. This nonexistence result, when combined with an existence theorem, yields in turn some information on topology, i.e. such an M has at most one p-hyperbolic end. Moreover, we prove a Liouville type theorem for strongly p-harmonic functions with finite q-energy on Riemannian manifolds, where the range for q contains p. As an application, we extend this theorem to some p-harmonic maps such as p-harmonic morphisms and conformal maps between Riemannian manifolds.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-10-30T01:53:24.000Z",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2016-02-23T03:04:03.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "p-harmonic maps",
      "finite q-energy",
      "liouville properties",
      "liouville type theorem",
      "riemannian manifolds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1211.2899C"
    }
  }
}