{
  "id": "0904.1781",
  "version": "v2",
  "published": "2009-04-11T07:06:05.000Z",
  "updated": "2014-06-24T22:58:45.000Z",
  "title": "Gradient estimates for the subelliptic heat kernel on H-type groups",
  "authors": [
    "Nathaniel Eldredge"
  ],
  "comment": "23 pages; updated with peer-review revisions",
  "journal": "Journal of Functional Analysis 258 (2010), pp. 504-533",
  "doi": "10.1016/j.jfa.2009.08.012",
  "categories": [
    "math.AP",
    "math.DG"
  ],
  "abstract": "We prove the following gradient inequality for the subelliptic heat kernel on nilpotent Lie groups $G$ of H-type: $$|\\nabla P_t f| \\le K P_t(|\\nabla f|)$$ where $P_t$ is the heat semigroup corresponding to the sublaplacian on $G$, $\\nabla$ is the subelliptic gradient, and $K$ is a constant. This extends a result of H.-Q. Li for the Heisenberg group. The proof is based on pointwise heat kernel estimates, and follows an approach used by Bakry, Baudoin, Bonnefont, and Chafa\\\"i.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-06-24T22:58:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35H10",
      "53C17"
    ],
    "keywords": [
      "subelliptic heat kernel",
      "h-type groups",
      "gradient estimates",
      "nilpotent lie groups",
      "pointwise heat kernel estimates"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0904.1781E"
    }
  }
}