{
  "id": "1408.6322",
  "version": "v1",
  "published": "2014-08-27T06:14:35.000Z",
  "updated": "2014-08-27T06:14:35.000Z",
  "title": "Needle decompositions in Riemannian geometry",
  "authors": [
    "Bo'az Klartag"
  ],
  "categories": [
    "math.DG",
    "math.MG"
  ],
  "abstract": "The localization technique from convex geometry is generalized to the setting of Riemannian manifolds whose Ricci curvature is bounded from below. In a nutshell, our method is based on the following observation: When the Ricci curvature is non-negative, log-concave measures are obtained when conditioning the Riemannian volume measure with respect to an integrable geodesic foliation. The Monge mass transfer problem plays an important role in our analysis.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-08-27T06:14:35.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "riemannian geometry",
      "needle decompositions",
      "monge mass transfer problem plays",
      "ricci curvature",
      "riemannian volume measure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1408.6322K"
    }
  }
}