{
  "id": "math/0412045",
  "version": "v3",
  "published": "2004-12-02T08:53:17.000Z",
  "updated": "2006-01-31T13:16:01.000Z",
  "title": "Global Gronwall Estimates for Integral Curves on Riemannian Manifolds",
  "authors": [
    "Michael Kunzinger",
    "Hermann Schichl",
    "Roland Steinbauer",
    "James A. Vickers"
  ],
  "comment": "4 pages, 1 figure, correction of some misprints",
  "journal": "Rev. Mat. Complut. 19 (2006), no. 1, 133--137.",
  "categories": [
    "math.DG",
    "math.CA"
  ],
  "abstract": "We prove Gronwall-type estimates for the distance of integral curves of smooth vector fields on a Riemannian manifold. Such estimates are of central importance for all methods of solving ODEs in a verified way, i.e., with full control of roundoff errors. Our results may therefore be seen as a prerequisite for the generalization of such methods to the setting of Riemannian manifolds.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2006-01-31T13:16:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53B21",
      "53C22",
      "34A26"
    ],
    "keywords": [
      "riemannian manifold",
      "global gronwall estimates",
      "integral curves",
      "smooth vector fields",
      "gronwall-type estimates"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math.....12045K"
    }
  }
}