{
  "id": "2007.07491",
  "version": "v1",
  "published": "2020-07-15T05:42:57.000Z",
  "updated": "2020-07-15T05:42:57.000Z",
  "title": "Convergence to the Product of the Standard Spheres and Eigenvalues of the Laplacian",
  "authors": [
    "Masayuki Aino"
  ],
  "comment": "28 pages",
  "categories": [
    "math.DG",
    "math.MG"
  ],
  "abstract": "We show a Gromov-Hausdorff approximation to the product of the standard spheres $S^{n-p}\\times S^p$ for Riemannian manifolds with positive Ricci curvature under some pinching condition on the eigenvalues of the Laplacian acting on functions and forms.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-07-15T05:42:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C20",
      "58J50"
    ],
    "keywords": [
      "standard spheres",
      "eigenvalues",
      "convergence",
      "gromov-hausdorff approximation",
      "positive ricci curvature"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}