{
  "id": "2402.02749",
  "version": "v2",
  "published": "2024-02-05T06:05:35.000Z",
  "updated": "2024-07-02T20:28:13.000Z",
  "title": "Loomis-Whitney inequalities on corank $1$ Carnot groups",
  "authors": [
    "Ye Zhang"
  ],
  "comment": "The final version of the article is published in Ann. Fenn. Math. 49(2): 437-459, 2024. doi:https://doi.org/10.54330/afm.146800",
  "journal": "Annales Fennici Mathematici, 49(2): 437-459, 2024",
  "doi": "10.54330/afm.146800",
  "categories": [
    "math.CA"
  ],
  "abstract": "In this paper we provide another way to deduce the Loomis-Whitney inequality on higher dimensional Heisenberg groups $\\mathbb{H}^n$ based on the one on the first Heisenberg group $\\mathbb{H}^1$ and the known nonlinear Loomis-Whitney inequality (which has more projections than ours). Moreover, we generalize the result to the case of corank $1$ Carnot groups and products of such groups. Our main tool is the modified equivalence between the Brascamp--Lieb inequality and the subadditivity of the entropy developed in arXiv:0710.0870v2.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2024-07-02T20:28:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "26D15",
      "28A75",
      "28D20",
      "39B62",
      "43A80"
    ],
    "keywords": [
      "carnot groups",
      "higher dimensional heisenberg groups",
      "first heisenberg group",
      "nonlinear loomis-whitney inequality",
      "main tool"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}