{
  "id": "1311.6584",
  "version": "v1",
  "published": "2013-11-26T08:24:44.000Z",
  "updated": "2013-11-26T08:24:44.000Z",
  "title": "The (B) conjecture for uniform measures in the plane",
  "authors": [
    "Amir Livne Bar-on"
  ],
  "comment": "10 pages",
  "categories": [
    "math.FA",
    "math.MG"
  ],
  "abstract": "We prove that for any two centrally-symmetric convex shapes $K,L \\subset \\mathbb{R}^2$, the function $t \\mapsto |e^t K \\cap L|$ is log-concave. This extends a result of Cordero-Erausquin, Fradelizi and Maurey in the two dimensional case. Possible relaxations of the condition of symmetry are discussed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-11-26T08:24:44.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "uniform measures",
      "conjecture",
      "centrally-symmetric convex shapes",
      "dimensional case",
      "cordero-erausquin"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1311.6584L"
    }
  }
}