{
  "id": "1802.06366",
  "version": "v1",
  "published": "2018-02-18T11:39:41.000Z",
  "updated": "2018-02-18T11:39:41.000Z",
  "title": "On the c-concavity with respect to the quadratic cost on a manifold",
  "authors": [
    "Federico Glaudo"
  ],
  "comment": "10 pages",
  "categories": [
    "math.OC",
    "math.DG"
  ],
  "abstract": "Pushing a little forward an approach proposed by Villani, we are going to prove that in the Riemannian setting the condition $\\nabla^2 f< g$ implies that $f$ is $c$-concave with respect to the quadratic cost as soon as it has a sufficiently small $C^1$-norm. From this, we deduce a sufficient condition for the optimality of transport maps.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-02-18T11:39:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "49Q20",
      "53C21"
    ],
    "keywords": [
      "quadratic cost",
      "c-concavity",
      "sufficient condition",
      "transport maps",
      "riemannian"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}