{
  "id": "0810.3218",
  "version": "v4",
  "published": "2008-10-17T19:25:30.000Z",
  "updated": "2016-12-01T21:19:50.000Z",
  "title": "Precise estimates for the subelliptic heat kernel on H-type groups",
  "authors": [
    "Nathaniel Eldredge"
  ],
  "comment": "35 pages. Identical to published version except that some typos are fixed here",
  "journal": "Journal de Math\\'ematiques Pures et Appliqu\\'ees 92 (2009), pp. 52-85",
  "doi": "10.1016/j.matpur.2009.04.011",
  "categories": [
    "math.AP",
    "math.DG"
  ],
  "abstract": "We establish precise upper and lower bounds for the subelliptic heat kernel on nilpotent Lie groups $G$ of H-type. Specifically, we show that there exist positive constants $C_1$, $C_2$ and a polynomial correction function $Q_t$ on $G$ such that $$C_1 Q_t e^{-\\frac{d^2}{4t}} \\le p_t \\le C_2 Q_t e^{-\\frac{d^2}{4t}}$$ where $p_t$ is the heat kernel, and $d$ the Carnot-Carath\\'eodory distance on $G$. We also obtain similar bounds on the norm of its subelliptic gradient $|\\nabla p_t|$. Along the way, we record explicit formulas for the distance function $d$ and the subriemannian geodesics of H-type groups.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2014-06-24T22:39:58.000Z",
      "comment": "49 pages, no figures"
    },
    {
      "version": "v4",
      "updated": "2016-12-01T21:19:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35H10",
      "53C17",
      "22E25",
      "58J99"
    ],
    "keywords": [
      "subelliptic heat kernel",
      "h-type groups",
      "precise estimates",
      "polynomial correction function",
      "nilpotent lie groups"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Elsevier"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0810.3218E"
    }
  }
}