{
  "id": "1701.08831",
  "version": "v1",
  "published": "2017-01-30T21:25:09.000Z",
  "updated": "2017-01-30T21:25:09.000Z",
  "title": "Jacobian determinant inequality on Corank 1 Carnot groups with applications",
  "authors": [
    "Zoltán M. Balogh",
    "Alexandru Kristály",
    "Kinga Sipos"
  ],
  "comment": "27 pages, 2 figures",
  "categories": [
    "math.AP"
  ],
  "abstract": "We establish a weighted pointwise Jacobian determinant inequality on corank 1 Carnot groups related to optimal mass transportation akin to the work of Cordero-Erausquin, McCann and Schmuckenschl\\\"ager. The weights appearing in our expression are distortion coefficients that reflect the delicate sub-Riemannian structure of our space including the presence of abnormal geodesics. Our inequality interpolates in some sense between Euclidean and sub-Riemannian structures, corresponding to the mass transportation along abnormal and strictly normal geodesics, respectively. As applications, entropy, Brunn-Minkowski and Borell-Brascamp-Lieb inequalities are established.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-01-30T21:25:09.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "carnot groups",
      "applications",
      "optimal mass transportation akin",
      "delicate sub-riemannian structure",
      "weighted pointwise jacobian determinant inequality"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}