{
  "id": "2110.09746",
  "version": "v3",
  "published": "2021-10-19T05:33:16.000Z",
  "updated": "2022-05-05T12:00:14.000Z",
  "title": "$C^{1,1}$-rectifiability and Heintze-Karcher inequality on $\\mathbf{S}^{n+1}$",
  "authors": [
    "Xuwen Zhang"
  ],
  "comment": "23 pages, 2 figures",
  "categories": [
    "math.AP",
    "math.DG"
  ],
  "abstract": "In this paper, by isometrically embedding $(\\mathbf{S}^{n+1},g_{\\mathbf{S}^{n+1}})$ into $\\mathbf{R}^{n+2}$, and using nonlinear analysis on the codimension-2 graphs, we will show that the level sets of distance function from the boundary of any Borel set in sphere, are $C^{1,1}$-rectifiable. As a by-product, we establish a Heintze-Karcher inequality.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2022-05-05T12:00:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B65",
      "49Q15",
      "49Q20",
      "53C21"
    ],
    "keywords": [
      "heintze-karcher inequality",
      "rectifiability",
      "borel set",
      "nonlinear analysis"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}