{
  "id": "0908.0442",
  "version": "v2",
  "published": "2009-08-04T13:26:18.000Z",
  "updated": "2012-10-05T12:41:48.000Z",
  "title": "Optimal Transport and Tessellation",
  "authors": [
    "Martin Huesmann"
  ],
  "comment": "corrected version, Theorem 2 appears in slightly different form in arXiv:1206.3672",
  "categories": [
    "math.PR"
  ],
  "abstract": "Optimal transport from the volume measure to a convex combination of Dirac measures yields a tessellation of a Riemannian manifold into pieces of arbitrary relative size. This tessellation is studied for the cost functions $c_p(z,y)=\\frac{1}{p}d^p(z,y)$ and $1\\leq p<\\infty$. Geometric descriptions of the tessellations for all $p$ is obtained for compact subsets of the Euclidean space. For $p=2$ this approach yields Laguerre tessellations. For $p=1$ it induces Johnson Mehl diagrams for all compact Riemannian manifolds.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-10-05T12:41:48.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "optimal transport",
      "induces johnson mehl diagrams",
      "approach yields laguerre tessellations",
      "compact riemannian manifolds",
      "dirac measures yields"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0908.0442H"
    }
  }
}