{
  "id": "1001.0147",
  "version": "v1",
  "published": "2009-12-31T16:23:59.000Z",
  "updated": "2009-12-31T16:23:59.000Z",
  "title": "Large scale geometry of negatively curved $\\R^n \\rtimes \\R$",
  "authors": [
    "Xiangdong Xie"
  ],
  "categories": [
    "math.GR",
    "math.CV"
  ],
  "abstract": "We classify all negatively curved $\\R^n \\rtimes \\R$ up to quasiisometry. We show that all quasiisometries between such manifolds (except when they are biLipschitz to the real hyperbolic spaces) are almost similarities. We prove these results by studying the quasisymmetric maps on the ideal boundary of these manifolds.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-12-31T16:23:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F65",
      "30C65"
    ],
    "keywords": [
      "large scale geometry",
      "real hyperbolic spaces",
      "ideal boundary",
      "quasisymmetric maps"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1001.0147X"
    }
  }
}