{
  "id": "1705.06789",
  "version": "v1",
  "published": "2017-05-18T20:27:35.000Z",
  "updated": "2017-05-18T20:27:35.000Z",
  "title": "Rigidity properties of the hypercube via Bakry-Emery curvature",
  "authors": [
    "Shiping Liu",
    "Florentin Münch",
    "Norbert Peyerimhoff"
  ],
  "comment": "29 pages, 8 figures",
  "categories": [
    "math.DG"
  ],
  "abstract": "We give rigidity results for the discrete Bonnet-Myers diameter bound and the Lichnerowicz eigenvalue estimate. Both inequalities are sharp if and only if the underlying graph is a hypercube. The proofs use well-known semigroup methods as well as new direct methods which translate curvature to combinatorial properties. Our results can be seen as first known discrete analogues of Cheng's and Obata's rigidity theorems.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-05-18T20:27:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C24",
      "05C35",
      "35K05"
    ],
    "keywords": [
      "bakry-emery curvature",
      "rigidity properties",
      "discrete bonnet-myers diameter bound",
      "lichnerowicz eigenvalue estimate",
      "well-known semigroup methods"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}