{
  "id": "0903.4842",
  "version": "v1",
  "published": "2009-03-27T16:26:46.000Z",
  "updated": "2009-03-27T16:26:46.000Z",
  "title": "Covering convex bodies by cylinders and lattice points by flats",
  "authors": [
    "Karoly Bezdek",
    "Alexander Litvak"
  ],
  "journal": "J. Geom. Anal. 19/2 (2009), 233-243",
  "doi": "10.1007/s12220-008-9063-6",
  "categories": [
    "math.MG"
  ],
  "abstract": "In connection with an unsolved problem of Bang (1951) we give a lower bound for the sum of the base volumes of cylinders covering a d-dimensional convex body in terms of the relevant basic measures of the given convex body. As an application we establish lower bounds on the number of k-dimensional flats (i.e. translates of k-dimensional linear subspaces) needed to cover all the integer points of a given convex body in d-dimensional Euclidean space for 0<k<d.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-03-27T16:26:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52A40",
      "46B07",
      "46B20",
      "52C17"
    ],
    "keywords": [
      "covering convex bodies",
      "lattice points",
      "d-dimensional euclidean space",
      "d-dimensional convex body",
      "relevant basic measures"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0903.4842B"
    }
  }
}