{
  "id": "0909.4361",
  "version": "v1",
  "published": "2009-09-24T04:22:42.000Z",
  "updated": "2009-09-24T04:22:42.000Z",
  "title": "Relative entropy of cone measures and $L_p$ centroid bodies",
  "authors": [
    "Grigoris Paouris",
    "Elisabeth M. Werner"
  ],
  "doi": "10.1112/plms/pdr030",
  "categories": [
    "math.FA"
  ],
  "abstract": "Let $K$ be a convex body in $\\mathbb R^n$. We introduce a new affine invariant, which we call $\\Omega_K$, that can be found in three different ways: as a limit of normalized $L_p$-affine surface areas, as the relative entropy of the cone measure of $K$ and the cone measure of $K^\\circ$, as the limit of the volume difference of $K$ and $L_p$-centroid bodies. We investigate properties of $\\Omega_K$ and of related new invariant quantities. In particular, we show new affine isoperimetric inequalities and we show a \"information inequality\" for convex bodies.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-09-24T04:22:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52A20",
      "53A15"
    ],
    "keywords": [
      "cone measure",
      "centroid bodies",
      "relative entropy",
      "convex body",
      "affine surface areas"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0909.4361P"
    }
  }
}