{
  "id": "1505.05817",
  "version": "v1",
  "published": "2015-05-21T18:14:44.000Z",
  "updated": "2015-05-21T18:14:44.000Z",
  "title": "Counterexamples Related to Rotations of Shadows of Convex Bodies",
  "authors": [
    "M. Angeles Alfonseca",
    "Michelle Cordier"
  ],
  "comment": "17 pages, 11 figures",
  "categories": [
    "math.MG"
  ],
  "abstract": "We construct examples of two convex bodies $K,L$ in $\\mathbb{R}^n$, such that every projection of $K$ onto a $(n-1)$-dimensional subspace can be rotated to be contained in the corresponding projection of $L$, but $K$ itself cannot be rotated to be contained in $L$. We also find necessary conditions on $K$ and $L$ to ensure that $K$ can be rotated to be contained in $L$ if all the $(n-1)$-dimensional projections have this property.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-05-21T18:14:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52A20",
      "52A38",
      "44A12"
    ],
    "keywords": [
      "convex bodies",
      "counterexamples",
      "dimensional projections",
      "construct examples",
      "necessary conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}