{
  "id": "1011.2911",
  "version": "v1",
  "published": "2010-11-12T14:10:36.000Z",
  "updated": "2010-11-12T14:10:36.000Z",
  "title": "Five lectures on optimal transportation: Geometry, regularity and applications",
  "authors": [
    "Nestor Guillen",
    "Robert McCann"
  ],
  "categories": [
    "math.AP",
    "math.DG"
  ],
  "abstract": "In this series of lectures we introduce the Monge-Kantorovich problem of optimally transporting one distribution of mass onto another, where optimality is measured against a cost function c(x,y). Connections to geometry, inequalities, and partial differential equations will be discussed, focusing in particular on recent developments in the regularity theory for Monge-Ampere type equations. An application to microeconomics will also be described, which amounts to finding the equilibrium price distribution for a monopolist marketing a multidimensional line of products to a population of anonymous agents whose preferences are known only statistically.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-11-12T14:10:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J96"
    ],
    "keywords": [
      "optimal transportation",
      "application",
      "partial differential equations",
      "monge-ampere type equations",
      "equilibrium price distribution"
    ],
    "tags": [
      "lecture notes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1011.2911G"
    }
  }
}