{
  "id": "math/0201247",
  "version": "v1",
  "published": "2002-01-25T15:08:47.000Z",
  "updated": "2002-01-25T15:08:47.000Z",
  "title": "Analytic Continuation of Holomorphic Correspondences and Equivalence of Domains in ${\\mathbb C}^n$",
  "authors": [
    "Rasul Shafikov"
  ],
  "comment": "17 pages",
  "doi": "10.1007/s00222-002-0282-3",
  "categories": [
    "math.CV"
  ],
  "abstract": "The following result is proved: Let $D$ and $D'$ be bounded domains in $\\mathbb C^n$, $\\partial D$ is smooth, real-analytic, simply connected, and $\\partial D'$ is connected, smooth, real-algebraic. Then there exists a proper holomorphic correspondence $f:D\\to D'$ if and only if $\\partial D$ and $\\partial D'$ a locally CR-equivalent. This leads to a characterization of the equivalence relationship between bounded domains in $\\mathbb C^n$ modulo proper holomorphic correspondences in terms of CR-equivalence of their boundaries.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2002-01-25T15:08:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "32H99"
    ],
    "keywords": [
      "analytic continuation",
      "modulo proper holomorphic correspondences",
      "bounded domains",
      "equivalence relationship",
      "locally cr-equivalent"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Inventiones Mathematicae",
      "year": 2003,
      "month": "Jun",
      "volume": 152,
      "number": 3,
      "pages": 665
    },
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003InMat.152..665S"
    }
  }
}