{
  "id": "1904.10765",
  "version": "v1",
  "published": "2019-04-24T12:32:51.000Z",
  "updated": "2019-04-24T12:32:51.000Z",
  "title": "Equipartitions and Mahler volumes of symmetric convex bodies",
  "authors": [
    "Matthieu Fradelizi",
    "Alfredo Hubard",
    "Mathieu Meyer",
    "Edgardo Roldán-Pensado",
    "Artem Zvavitch"
  ],
  "comment": "7 pages, 1 figure",
  "categories": [
    "math.MG"
  ],
  "abstract": "Following ideas of Iriyeh and Shibata we give a short proof of the three-dimensional symmetric Mahler conjecture. Our contributions are simple self-contained proofs of their two key statements. The first of these is an equipartition (ham sandwich type) theorem which refines a celebrated result of Hadwiger and, as usual, can be proved using ideas from equivariant topology. The second is an inequality relating the product volume to areas of certain sections and their duals. Finally, we observe that these ideas give a large family of convex sets in every dimension for which the Mahler conjecture holds true.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-04-24T12:32:51.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "symmetric convex bodies",
      "mahler volumes",
      "equipartition",
      "mahler conjecture holds true",
      "three-dimensional symmetric mahler conjecture"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}