{
  "id": "2204.13018",
  "version": "v1",
  "published": "2022-04-27T15:56:42.000Z",
  "updated": "2022-04-27T15:56:42.000Z",
  "title": "New invariants of Gromov-Hausdorff limits of Riemannian surfaces with curvature bounded below",
  "authors": [
    "Semyon Alesker",
    "Mikhail Katz",
    "Roman Prosanov"
  ],
  "comment": "50 pages",
  "categories": [
    "math.DG",
    "math.MG"
  ],
  "abstract": "Let $\\{X_i\\}$ be a sequence of compact $n$-dimensional Alexandrov spaces (e.g. Riemannian manifolds) with curvature uniformly bounded below which converges in the Gromov-Hausdorff sense to a compact Alexandrov space $X$. In an earlier paper by the first author there was described (without a proof) a construction of an integer valued function on $X$; this function carries additional geometric information on the sequence such as the limit of intrinsic volumes of $X_i$'s. In this paper we consider sequences of closed 2-surfaces and (1) prove the existence of such a function in this situation; and (2) classify the functions which may arise from the construction.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-04-27T15:56:42.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "riemannian surfaces",
      "gromov-hausdorff limits",
      "function carries additional geometric information",
      "invariants",
      "compact alexandrov space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 50,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}