{
  "id": "1301.3663",
  "version": "v1",
  "published": "2013-01-16T11:45:40.000Z",
  "updated": "2013-01-16T11:45:40.000Z",
  "title": "Approximation of the spectrum of a manifold by discretization",
  "authors": [
    "Erwann Aubry"
  ],
  "categories": [
    "math.AP",
    "math.DG",
    "math.SP"
  ],
  "abstract": "We approximate the spectral data (eigenvalues and eigenfunctions) of compact Riemannian manifold by the spectral data of a sequence of (computable) discrete Laplace operators associated to some graphs immersed in the manifold. We give an upper bound on the error that depends on upper bounds on the diameter and the sectional curvature and on a lower bound on the injectivity radius.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-01-16T11:45:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "approximation",
      "discretization",
      "spectral data",
      "upper bound",
      "compact riemannian manifold"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1301.3663A"
    }
  }
}