{
  "id": "2306.02581",
  "version": "v1",
  "published": "2023-06-05T04:13:41.000Z",
  "updated": "2023-06-05T04:13:41.000Z",
  "title": "Stability of Alexandrov-Fenchel Type Inequalities for Nearly Spherical Sets in Space Forms",
  "authors": [
    "Rong Zhou",
    "Tailong Zhou"
  ],
  "comment": "25 pages",
  "categories": [
    "math.DG"
  ],
  "abstract": "In this paper, we first derive a quantitative quermassintegral inequality for nearly spherical sets in $\\mathbb{H}^{n+1}$ and $\\mathbb{S}^{n+1}$, which is a generalization of the inequality proved in $\\mathbb{R}^{n+1}$ [21]. Then we use this method to derive the stability of some geometric inequalities involving weighted curvature integrals and quermassintegrals for nearly spherical sets in $\\mathbb{R}^{n+1}$ and $\\mathbb{H}^{n+1}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-06-05T04:13:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52A40",
      "53C42"
    ],
    "keywords": [
      "alexandrov-fenchel type inequalities",
      "spherical sets",
      "space forms",
      "quantitative quermassintegral inequality",
      "geometric inequalities"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}