{
  "id": "1407.0809",
  "version": "v1",
  "published": "2014-07-03T08:01:09.000Z",
  "updated": "2014-07-03T08:01:09.000Z",
  "title": "Nonsmooth differential geometry - An approach tailored for spaces with Ricci curvature bounded from below",
  "authors": [
    "Nicola Gigli"
  ],
  "categories": [
    "math.DG",
    "math.MG"
  ],
  "abstract": "We discuss in which sense general metric measure spaces possess a first order differential structure. Building on this, we then see that on spaces with Ricci curvature bounded from below a second order calculus can be developed, permitting to define Hessian, covariant/exterior derivatives and Ricci curvature.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-07-03T08:01:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "51Fxx"
    ],
    "keywords": [
      "ricci curvature",
      "nonsmooth differential geometry",
      "general metric measure spaces possess",
      "sense general metric measure spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1407.0809G"
    }
  }
}