{
  "id": "math/0503290",
  "version": "v1",
  "published": "2005-03-15T07:02:53.000Z",
  "updated": "2005-03-15T07:02:53.000Z",
  "title": "Centroids and comparison of volumes",
  "authors": [
    "V. Yaskin",
    "M. Yaskina"
  ],
  "comment": "18 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "For $-1<p<1$ we introduce the concept of a polar $p$-centroid body ${\\Gamma^*_p K}$ of a star body $K$. We consider the question of whether ${\\Gamma^*_p K}\\subset {\\Gamma^*_p L}$ implies $\\mathrm{vol}(L)\\le \\mathrm{vol}(K).$ Our results extend the studies by Lutwak in the case $p=1$ and Grinberg, Zhang in the case $p> 1$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-03-15T07:02:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52Axx"
    ],
    "keywords": [
      "comparison",
      "centroid body",
      "star body",
      "results extend"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......3290Y"
    }
  }
}