{
  "id": "0903.0169",
  "version": "v1",
  "published": "2009-03-01T19:46:38.000Z",
  "updated": "2009-03-01T19:46:38.000Z",
  "title": "Finiteness of the number of ends of minimal submanifolds in euclidean space",
  "authors": [
    "Vladimir G. Tkachev"
  ],
  "comment": "18 pages",
  "journal": "Manuscr. Math., 82(1994), no 1, 313-330",
  "doi": "10.1007/BF02567704",
  "categories": [
    "math.DG",
    "math.GT"
  ],
  "abstract": "We prove a version of the well-known Denjoy-Ahlfors theorem about the number of asymptotic values of an entire function for properly immersed minimal surfaces of arbitrary codimension in R^N. The finiteness of the number of ends is proved for minimal submanifolds with finite projective volume. We show, as a corollary, that a minimal surface of codimensionn meeting any n-plane passing through the origin in at most k points has no more c(n,N)k ends.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-03-01T19:46:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53A10",
      "49Q05",
      "53C65"
    ],
    "keywords": [
      "minimal submanifolds",
      "euclidean space",
      "finiteness",
      "well-known denjoy-ahlfors theorem",
      "finite projective volume"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Springer",
      "journal": "Commun. Math. Phys."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0903.0169T"
    }
  }
}