{
  "id": "1612.00295",
  "version": "v1",
  "published": "2016-12-01T15:04:54.000Z",
  "updated": "2016-12-01T15:04:54.000Z",
  "title": "On the monotonicity of perimeter of convex bodies",
  "authors": [
    "Giorgio Stefani"
  ],
  "comment": "8 pages",
  "categories": [
    "math.MG"
  ],
  "abstract": "Let $n\\ge2$ and let $\\Phi\\colon\\mathbb{R}^n\\to[0,\\infty)$ be a positively $1$-homogeneous and convex function. Given two convex bodies $A\\subset B$ in $\\mathbb{R}^n$, the monotonicity of anisotropic $\\Phi$-perimeters holds, i.e. $P_\\Phi(A)\\le P_\\Phi(B)$. In this note, we prove a quantitative lower bound on the difference of the $\\Phi$-perimeters of $A$ and $B$ in terms of their Hausdorff distance.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-12-01T15:04:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52A20",
      "52A40"
    ],
    "keywords": [
      "convex bodies",
      "monotonicity",
      "convex function",
      "perimeters holds",
      "quantitative lower bound"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}