{
  "id": "1906.09599",
  "version": "v1",
  "published": "2019-06-23T15:55:58.000Z",
  "updated": "2019-06-23T15:55:58.000Z",
  "title": "$L_p$ functional Busemann-Petty centroid inequality",
  "authors": [
    "Julian Haddad",
    "Carlos Hugo Jimenez",
    "Leticia Alves da Silva"
  ],
  "comment": "14 pages. Comments are welcome",
  "categories": [
    "math.FA",
    "math.MG"
  ],
  "abstract": "If $K\\subset\\mathbb{R}^n$ is a convex body and $\\Gamma_pK$ is the $p$-centroid body of $K$, the $L_p$ Busemann-Petty centroid inequality states that $\\vol(\\Gamma_pK) \\geq \\vol(K)$, with equality if and only if $K$ is an ellipsoid centered at the origin. In this work, we prove inequalities for a type of functional $r$-mixed volume for $1 \\leq r < n$, and establish as a consequence, a functional version of the $L_p$ Busemann-Petty centroid inequality. \\keywords{Convex body, Moment body, Busemann-Petty centroid} }",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-06-23T15:55:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "39B62"
    ],
    "keywords": [
      "functional busemann-petty centroid inequality",
      "busemann-petty centroid inequality states",
      "centroid body",
      "moment body",
      "functional version"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}