{
  "id": "1106.3736",
  "version": "v7",
  "published": "2011-06-19T12:11:02.000Z",
  "updated": "2020-10-17T00:30:00.000Z",
  "title": "Sweeping out sectional curvature",
  "authors": [
    "D. Panov",
    "A. Petrunin"
  ],
  "comment": "+minor corrections",
  "journal": "Geom. Topol. 18 (2014) 617-631",
  "doi": "10.2140/gt.2014.18.617",
  "categories": [
    "math.DG"
  ],
  "abstract": "We observe that the maximal open set of constant curvature k in a Riemannian manifold with curvature bounded below or above by k has a convexity type property, which we call \"two-convexity\". This statement is used to prove a number of rigidity statements in comparison geometry.",
  "revisions": [
    {
      "version": "v6",
      "updated": "2013-11-27T00:02:51.000Z",
      "journal": "Geom. Topol. 18 (2014), no. 2, 617--631",
      "doi": null
    },
    {
      "version": "v7",
      "updated": "2020-10-17T00:30:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C20",
      "53C24"
    ],
    "keywords": [
      "sectional curvature",
      "maximal open set",
      "convexity type property",
      "riemannian manifold",
      "constant curvature"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1106.3736P"
    }
  }
}