{
  "id": "1011.0869",
  "version": "v2",
  "published": "2010-11-03T13:08:14.000Z",
  "updated": "2012-04-13T11:29:20.000Z",
  "title": "Extensions of theorems of Rattray and Makeev",
  "authors": [
    "Pavle Blagojević",
    "Roman Karasev"
  ],
  "journal": "Topological Methods in Nonlinear Analysis 40:1(2012), 189-213",
  "categories": [
    "math.AT",
    "math.FA",
    "math.MG"
  ],
  "abstract": "We consider extensions of the Rattray theorem and two Makeev's theorems, showing that they hold for several maps, measures, or functions simultaneously, when we consider orthonormal $k$-frames in $\\R^n$ instead of orthonormal basis (full frames). We also present new results on simultaneous partition of several measures into parts by $k$ mutually orthogonal hyperplanes. In the case $k=2$ we relate the Rattray and Makeev type results with the well known embedding problem for projective spaces.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-04-13T11:29:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55M20",
      "05D10",
      "20J06",
      "46B20",
      "52A21",
      "55M35"
    ],
    "keywords": [
      "extensions",
      "makeev type results",
      "rattray theorem",
      "full frames",
      "mutually orthogonal hyperplanes"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1011.0869B"
    }
  }
}