{
  "id": "1104.5128",
  "version": "v1",
  "published": "2011-04-27T12:44:38.000Z",
  "updated": "2011-04-27T12:44:38.000Z",
  "title": "Quasihyperbolic geodesics in John domains in R^n",
  "authors": [
    "Manzi Huang",
    "Xiantao Wang"
  ],
  "comment": "17 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "In this paper, we prove that if $D\\subset R^n$ is a John domain which is homeomorphic to a uniform domain via a quasiconformal mapping, then each quasihyperbolic geodesic in $D$ is a cone arc, which shows that the answer to one of open problems raised by Heinonen in \\cite{H} is affirmative. This result also shows that the answer to the open problem raised by Gehring, Hag and Martio in \\cite{Gm} is positive for John domains which are homeomorphic to uniform domains via uasiconformal mappings. As an application, we prove that if $D\\subset R^n$ is a John domain which is homeomorphic to a uniform domain, then $D$ must be a quasihyperbolic $(b, \\lambda)$-uniform domain.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-04-27T12:44:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "30C65",
      "30F45",
      "30C20"
    ],
    "keywords": [
      "john domain",
      "quasihyperbolic geodesic",
      "uniform domain",
      "homeomorphic",
      "cone arc"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1104.5128H"
    }
  }
}