{
  "id": "2203.14626",
  "version": "v1",
  "published": "2022-03-28T10:28:39.000Z",
  "updated": "2022-03-28T10:28:39.000Z",
  "title": "A proof of Toponogov's theorem in Alexandrov geometry",
  "authors": [
    "Shengqi Hu",
    "Xiaole Su",
    "Yusheng Wang"
  ],
  "comment": "5 pages",
  "categories": [
    "math.DG",
    "math.MG"
  ],
  "abstract": "This paper aims to give an elementary proof for Toponogov's theorem in Alexandrov geometry with lower curvature bound. The idea of the proof comes from the fact that, in Riemannian geometry, sectional curvature can be embodied in the second variation formula.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-03-28T10:28:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C20",
      "51F99"
    ],
    "keywords": [
      "toponogovs theorem",
      "alexandrov geometry",
      "second variation formula",
      "lower curvature bound",
      "elementary proof"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}