{
  "id": "2101.03307",
  "version": "v1",
  "published": "2021-01-09T07:06:49.000Z",
  "updated": "2021-01-09T07:06:49.000Z",
  "title": "Anisotropic perimeter and isoperimetric quotient of inner parallel bodies",
  "authors": [
    "Graziano Crasta"
  ],
  "comment": "5 pages",
  "categories": [
    "math.MG",
    "math.FA"
  ],
  "abstract": "The aim of this note is twofold: to give a short proof of the results in [S. Larson, A bound for the perimeter of inner parallel bodies, J. Funct. Anal. 271 (2016), 610-619] and [G. Domokos and Z. L\\'angi, The isoperimetric quotient of a convex body decreases monotonically under the eikonal abrasion model, Mathematika 65 (2019), 119-129]; and to generalize them to the anisotropic case.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-01-09T07:06:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52A20",
      "52A38",
      "52A39"
    ],
    "keywords": [
      "inner parallel bodies",
      "isoperimetric quotient",
      "anisotropic perimeter",
      "convex body decreases",
      "eikonal abrasion model"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}