{
  "id": "2108.01476",
  "version": "v1",
  "published": "2021-08-03T13:04:14.000Z",
  "updated": "2021-08-03T13:04:14.000Z",
  "title": "Anisotropic curvature measures and uniqueness of convex bodies",
  "authors": [
    "Mario Santilli"
  ],
  "categories": [
    "math.MG",
    "math.DG"
  ],
  "abstract": "We prove that an arbitrary convex body $C \\subseteq \\mathbf{R}^{n+1} $, whose $ k $-th anisotropic curvature measure (for $ k =0, \\ldots , n-1 $) is a multiple constant of the anisotropic perimeter of C, must be a rescaled and translated Wulff shape.This result provides a generalization of a theorem of Schneider (1979) and resolves a conjecture of Andrews and Wei (2017).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-08-03T13:04:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52A20",
      "52A39",
      "53E10"
    ],
    "keywords": [
      "uniqueness",
      "th anisotropic curvature measure",
      "arbitrary convex body",
      "multiple constant",
      "anisotropic perimeter"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}