{
  "id": "1101.5146",
  "version": "v3",
  "published": "2011-01-26T20:26:27.000Z",
  "updated": "2012-02-04T18:17:06.000Z",
  "title": "Regularity for the optimal transportation problem with Euclidean distance squared cost on the embedded sphere",
  "authors": [
    "Jun Kitagawa",
    "Micah Warren"
  ],
  "comment": "15 pages. Added gradient estimate depending on Wasserstein distance (see section 5)",
  "categories": [
    "math.AP",
    "math.DG"
  ],
  "abstract": "We give sufficient conditions on initial and target measures supported on the sphere $\\S^n$ to ensure the solution to the optimal transport problem with the cost $|x-y|^2/2$ is a diffeomorphism.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2012-02-04T18:17:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "49Q20",
      "35J96"
    ],
    "keywords": [
      "euclidean distance squared cost",
      "optimal transportation problem",
      "embedded sphere",
      "regularity",
      "optimal transport problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}