{
  "id": "1508.07105",
  "version": "v1",
  "published": "2015-08-28T06:22:06.000Z",
  "updated": "2015-08-28T06:22:06.000Z",
  "title": "A Remark on Regular Points of Ricci Limit Spaces",
  "authors": [
    "Lina Chen"
  ],
  "categories": [
    "math.DG"
  ],
  "abstract": "Let $Y$ be a Gromov-Hausdorff limit of complete Riemannian n-manifolds with Ricci curvature bounded from below. A point in $Y$ is called $k$-regular, if its tangent is unique and is isometric to an $k$-dimensional Euclidean space. By \\cite{B5}, there is $k>0$ such that the set of all $k$-regular point $\\mathcal{R}_k$ has a full renormalized measure. An open problem is if $\\mathcal{R}_l=\\emptyset$ for all $l<k$? The main result in this paper asserts that if $\\mathcal{R}_1\\ne \\emptyset$, then $Y$ is a one dimensional topological manifold. Our result improves the Handa's result \\cite{Honda} that under the assumption that $1\\leq \\mathrm{dim}_H(Y)<2$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-08-28T06:22:06.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "ricci limit spaces",
      "regular point",
      "dimensional euclidean space",
      "complete riemannian n-manifolds",
      "handas result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}