{
  "id": "1207.7286",
  "version": "v1",
  "published": "2012-07-31T15:21:33.000Z",
  "updated": "2012-07-31T15:21:33.000Z",
  "title": "Rotation invariant Minkowski classes of convex bodies",
  "authors": [
    "Rolf Schneider",
    "Franz E. Schuster"
  ],
  "journal": "Mathematika 54 (2007), 1-13",
  "categories": [
    "math.MG",
    "math.DG",
    "math.FA"
  ],
  "abstract": "A Minkowski class is a closed subset of the space of convex bodies in Euclidean space Rn which is closed under Minkowski addition and non-negative dilatations. A convex body in Rn is universal if the expansion of its support function in spherical harmonics contains non-zero harmonics of all orders. If K is universal, then a dense class of convex bodies M has the following property. There exist convex bodies T1; T2 such that M + T1 = T2, and T1; T2 belong to the rotation invariant Minkowski class generated by K. It is shown that every convex body K which is not centrally symmetric has a linear image, arbitrarily close to K, which is universal. A modified version of the result holds for centrally symmetric convex bodies. In this way, a result of S. Alesker is strengthened, and at the same time given a more elementary proof.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-07-31T15:21:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52A20",
      "33C55"
    ],
    "keywords": [
      "convex body",
      "rotation invariant minkowski classes",
      "spherical harmonics contains non-zero harmonics"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1207.7286S"
    }
  }
}