{
  "id": "2405.18501",
  "version": "v1",
  "published": "2024-05-28T18:14:00.000Z",
  "updated": "2024-05-28T18:14:00.000Z",
  "title": "Small volume bodies of constant width",
  "authors": [
    "Andrii Arman",
    "Andriy Bondarenko",
    "Fedor Nazarov",
    "Andriy Prymak",
    "Danylo Radchenko"
  ],
  "comment": "7 pages, 2 figures",
  "categories": [
    "math.MG"
  ],
  "abstract": "For every large enough $n$, we explicitly construct a body of constant width $2$ that has volume less than $0.9^n \\text{Vol}(\\mathbb{B}^{n}$), where $\\mathbb{B}^{n}$ is the unit ball in $\\mathbb{R}^{n}$. This answers a question of O.~Schramm.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-05-28T18:14:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52A20",
      "52A40",
      "28A75",
      "49Q20"
    ],
    "keywords": [
      "small volume bodies",
      "constant width",
      "unit ball",
      "explicitly construct"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}