{
  "id": "math/9201204",
  "version": "v1",
  "published": "1989-10-26T14:59:00.000Z",
  "updated": "1989-10-26T14:59:00.000Z",
  "title": "Shadows of convex bodies",
  "authors": [
    "Keith Ball"
  ],
  "categories": [
    "math.MG",
    "math.FA"
  ],
  "abstract": "It is proved that if $C$ is a convex body in ${\\Bbb R}^n$ then $C$ has an affine image $\\widetilde C$ (of non-zero volume) so that if $P$ is any 1-codimensional orthogonal projection, $$|P\\widetilde C| \\ge |\\widetilde C|^{n-1\\over n}.$$ It is also shown that there is a pathological body, $K$, all of whose orthogonal projections have volume about $\\sqrt{n}$ times as large as $|K|^{n-1\\over n}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1989-10-26T14:59:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52A20",
      "52A40"
    ],
    "keywords": [
      "convex body",
      "orthogonal projection",
      "affine image",
      "non-zero volume"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}