{
  "id": "1307.2658",
  "version": "v2",
  "published": "2013-07-10T03:00:29.000Z",
  "updated": "2013-07-23T03:55:30.000Z",
  "title": "Comparison principle, stochastic completeness and half-space theorems",
  "authors": [
    "G. Pacelli Bessa",
    "Jorge H. de Lira",
    "Adriano A. Medeiros"
  ],
  "comment": "We added two references and corrected few misprints",
  "categories": [
    "math.DG"
  ],
  "abstract": "We present a criterion for the stochastic completeness of a submanifold in terms of its distance to a hypersurface in the ambient space. This relies in a suitable version of the Hessian comparison theorem. In the sequel we apply a comparison principle with geometric barriers for establishing mean curvature estimates for stochastically complete submanifolds in Riemannian products, Riemannian submersions and wedges. These estimates are applied for obtaining both horizontal and vertical half-space theorems for submanifolds in $\\mathbb{H}^n \\times \\mathbb{R}^\\ell$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-07-23T03:55:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C42",
      "53C21"
    ],
    "keywords": [
      "comparison principle",
      "stochastic completeness",
      "establishing mean curvature estimates",
      "hessian comparison theorem",
      "stochastically complete submanifolds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1307.2658P"
    }
  }
}