{
  "id": "math/0701723",
  "version": "v2",
  "published": "2007-01-25T04:00:03.000Z",
  "updated": "2007-01-27T14:49:02.000Z",
  "title": "Degenerations of Riemannian manifolds",
  "authors": [
    "Igor Belegradek"
  ],
  "comment": "references added, 11 pages",
  "categories": [
    "math.DG"
  ],
  "abstract": "This is an expositiry article on collapsing theory in Riemannian geometry written for the Modern Encyclopedia of Mathematical Physics (MEMPhys). We focus on describing the geometric and topological structure of collapsed/non-collapsed regions in Riemannian manifold under various curvature assumptions. Numerous applications of collapsing theory to Riemannian geometry are NOT discussed in this survey.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2007-01-27T14:49:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C20"
    ],
    "keywords": [
      "riemannian manifold",
      "degenerations",
      "collapsing theory",
      "riemannian geometry written",
      "curvature assumptions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007math......1723B"
    }
  }
}