{
  "id": "math/0612532",
  "version": "v1",
  "published": "2006-12-18T23:34:57.000Z",
  "updated": "2006-12-18T23:34:57.000Z",
  "title": "Some Geometry and Analysis on Ricci Solitons",
  "authors": [
    "Aaron Naber"
  ],
  "comment": "8 pages",
  "categories": [
    "math.DG"
  ],
  "abstract": "The Bakry-Emery Ricci tensor of a metric-measure space (M,g,e^{-f}dv_{g}) plays an important role in both geometric measure theory and the study of Hamilton's Ricci flow. Under a uniform positivity condition on this tensor and with bounded Ricci curvature we show the underlying space has finite f-volume. As a consequence such manifolds, including shrinking Ricci solitons, have finite fundamental group. The analysis can be extended to classify shrinking solitons under convexity or concavity assumptions on the measure function.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-12-18T23:34:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C21",
      "53C44"
    ],
    "keywords": [
      "bakry-emery ricci tensor",
      "finite fundamental group",
      "geometric measure theory",
      "hamiltons ricci flow",
      "uniform positivity condition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math.....12532N"
    }
  }
}