{
  "id": "0706.1120",
  "version": "v2",
  "published": "2007-06-08T07:31:16.000Z",
  "updated": "2007-09-14T21:28:13.000Z",
  "title": "Comparison Geometry for the Bakry-Emery Ricci Tensor",
  "authors": [
    "Guofang Wei",
    "Will Wylie"
  ],
  "comment": "21 pages, Some of the estimates have been improved. In light of some new references, and to improve the exposition, the paper has been reorganized. An appendix is also added",
  "categories": [
    "math.DG"
  ],
  "abstract": "For Riemannian manifolds with a measure $(M,g, e^{-f} dvol_g)$ we prove mean curvature and volume comparison results when the $\\infty$-Bakry-Emery Ricci tensor is bounded from below and $f$ is bounded or $\\partial_r f$ is bounded from below, generalizing the classical ones (i.e. when $f$ is constant). This leads to extensions of many theorems for Ricci curvature bounded below to the Bakry-Emery Ricci tensor. In particular, we give extensions of all of the major comparison theorems when $f$ is bounded. Simple examples show the bound on $f$ is necessary for these results.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2007-09-14T21:28:13.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "bakry-emery ricci tensor",
      "comparison geometry",
      "major comparison theorems",
      "volume comparison results",
      "mean curvature"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0706.1120W"
    }
  }
}