{
  "id": "2007.02665",
  "version": "v1",
  "published": "2020-07-06T11:50:42.000Z",
  "updated": "2020-07-06T11:50:42.000Z",
  "title": "Weak formulation of the MTW condition and convexity properties of potentials",
  "authors": [
    "G. Loeper",
    "N. S. Trudinger"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We simplify the geometric interpretation of the weak Ma-Trudinger-Wang condition for regularity in optimal transportation and provide a geometric proof of the global c-convexity of locally $c$-convex potentials when the cost function $c$ is only assumed twice differentiable.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-07-06T11:50:42.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "weak formulation",
      "mtw condition",
      "convexity properties",
      "weak ma-trudinger-wang condition",
      "geometric interpretation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}