{
  "id": "0708.0269",
  "version": "v2",
  "published": "2007-08-02T04:20:42.000Z",
  "updated": "2013-09-30T03:36:29.000Z",
  "title": "Sharp k-order Sobolev inequalities in the hyperbolic space ${\\Bbb H}^n$",
  "authors": [
    "Genqian Liu"
  ],
  "comment": "20 pages",
  "categories": [
    "math.AP",
    "math.DG"
  ],
  "abstract": "In this paper, we obtain the sharp $k$-th order Sobolev inequalities in the hyperbolic space ${\\H}^n$ for all $k=1,2,3,\\cdots$. This gives an answer to an open question raised by Aubin in [5, p.$\\;$176-177] for $W^{k,2}({\\H}^n)$ with $k>1$. In addition, we prove that the associated Sobolev constants are optimal.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-09-30T03:36:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46E35",
      "35J35",
      "35J60"
    ],
    "keywords": [
      "sharp k-order sobolev inequalities",
      "hyperbolic space",
      "th order sobolev inequalities",
      "open question",
      "associated sobolev constants"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0708.0269L"
    }
  }
}