{
  "id": "0810.0149",
  "version": "v2",
  "published": "2008-10-01T12:44:14.000Z",
  "updated": "2008-11-26T15:49:17.000Z",
  "title": "Bounds on the volume entropy and simplicial volume in Ricci curvature $L^p$ bounded from below",
  "authors": [
    "E. Aubry"
  ],
  "categories": [
    "math.DG"
  ],
  "abstract": "Let $(M,g)$ be a compact manifold with Ricci curvature almost bounded from below and $\\pi:\\bar{M}\\to M$ be a normal, Riemannian cover. We show that, for any nonnegative function $f$ on $M$, the means of $f\\o\\pi$ on the geodesic balls of $\\bar{M}$ are comparable to the mean of $f$ on $M$. Combined with logarithmic volume estimates, this implies bounds on several topological invariants (volume entropy, simplicial volume, first Betti number and presentations of the fundamental group) in Ricci curvature $L^p$-bounded from below.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-11-26T15:49:17.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "ricci curvature",
      "simplicial volume",
      "volume entropy",
      "logarithmic volume estimates",
      "first betti number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0810.0149A"
    }
  }
}