{
  "id": "0908.2891",
  "version": "v1",
  "published": "2009-08-20T09:55:46.000Z",
  "updated": "2009-08-20T09:55:46.000Z",
  "title": "Transportation-Cost Inequalities on Path Space Over Manifolds with Boundary",
  "authors": [
    "Feng-Yu Wang"
  ],
  "comment": "26 pages",
  "categories": [
    "math.PR",
    "math.DG"
  ],
  "abstract": "Let $L=\\DD+Z$ for a $C^1$ vector field $Z$ on a complete Riemannian manifold possibly with a boundary. By using the uniform distance, a number of transportation-cost inequalities on the path space for the (reflecting) $L$-diffusion process are proved to be equivalent to the curvature condition $\\Ric-\\nn Z\\ge - K$ and the convexity of the boundary (if exists). These inequalities are new even for manifolds without boundary, and are partly extended to non-convex manifolds by using a conformal change of metric which makes the boundary from non-convex to convex.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-08-20T09:55:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J60",
      "58G60"
    ],
    "keywords": [
      "path space",
      "transportation-cost inequalities",
      "vector field",
      "conformal change",
      "uniform distance"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0908.2891W"
    }
  }
}