{
  "id": "2307.03208",
  "version": "v1",
  "published": "2023-07-06T09:43:03.000Z",
  "updated": "2023-07-06T09:43:03.000Z",
  "title": "On a formula for all sets of constant width in 3d",
  "authors": [
    "Bernd Kawohl",
    "Guido Sweers"
  ],
  "comment": "19 pages, 10 figures",
  "categories": [
    "math.MG"
  ],
  "abstract": "In the recent paper \"On a formula for sets of constant width in 2D\", Comm. Pure Appl. Anal. 18 (2019), 2117-2131, we gave a constructive formula for all 2d sets of constant width. Based on this result we derive here a formula for the parametrization of the boundary of bodies of constant width in 3 dimensions, depending on one function defined on S^2 and a large enough constant. Moreover, we show that all bodies of constant width in 3d have such a parametrization. The last result needs a tool that we describe as `shadow domain' and that is explained in an appendix. Our formula is more explicit than the result by T. Bayen, T. Lachand-Robert and \\'E. Oudet, \"Analytic parametrization of three-dimensional bodies of constant width\" in Arch. Ration. Mech. Anal., 186 (2007), 225-249.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-07-06T09:43:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52A15"
    ],
    "keywords": [
      "constant width",
      "pure appl",
      "three-dimensional bodies",
      "result needs",
      "shadow domain"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}