{
  "id": "1211.3621",
  "version": "v3",
  "published": "2012-11-15T14:53:04.000Z",
  "updated": "2017-08-16T15:42:55.000Z",
  "title": "Diffusion semigroup on manifolds with time-dependent metrics",
  "authors": [
    "Li-Juan Cheng"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "Let $L_t:=\\Delta_t +Z_t $, $t\\in [0,T_c)$ on a differential manifold equipped with time-depending complete Riemannian metric $(g_t)_{t\\in [0,T_c)}$, where $\\Delta_t$ is the Laplacian induced by $g_t$ and $(Z_t)_{t\\in [0,T_c)}$ is a family of $C^{1,1}$-vector fields. We first present some explicit criteria for the non-explosion of the diffusion processes generated by $L_t$; then establish the derivative formula for the associated semigroup; and finally, present a number of equivalent semigroup inequalities for the curvature lower bound condition, which include the gradient inequalities, transportation-cost inequalities, Harnack inequalities and functional inequalities for the diffusion semigroup.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-06-20T14:19:48.000Z",
      "title": "Diffusion Process on Time-Inhomogeneous Manifolds",
      "comment": null,
      "journal": null,
      "doi": null,
      "authors": [
        "Lijuan Cheng"
      ]
    },
    {
      "version": "v3",
      "updated": "2017-08-16T15:42:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J60",
      "58J65",
      "53C44"
    ],
    "keywords": [
      "diffusion process",
      "time-inhomogeneous manifolds",
      "curvature lower bound condition",
      "time-depending complete riemannian metric",
      "equivalent semigroup inequalities"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1211.3621C"
    }
  }
}