{
  "id": "2104.03051",
  "version": "v1",
  "published": "2021-04-07T11:01:36.000Z",
  "updated": "2021-04-07T11:01:36.000Z",
  "title": "Euclidean domains in complex manifolds",
  "authors": [
    "Franc Forstneric"
  ],
  "categories": [
    "math.CV"
  ],
  "abstract": "In this paper we find big Euclidean domains in complex manifolds. We consider open neighbourhoods of sets of the form $K\\cup M$ in a complex manifold $X$, where $K$ is a Stein compact, $M$ is an embedded Stein submanifold of $X$, and $K\\cap M$ is compact and $\\mathscr O(M)$-convex. We prove a Docquier-Grauert type theorem concerning biholomorphic equivalence of neighbourhoods of such sets, and we give sufficient conditions for the existence of Stein neighbourhoods of $K\\cup M$, biholomorphic to domains in $\\mathbb C^n$ with $n=\\dim X$, such that $M$ is mapped onto a closed complex submanifold of $\\mathbb C^n$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-04-07T11:01:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "32E10",
      "32E30",
      "32H02",
      "32Q56"
    ],
    "keywords": [
      "complex manifold",
      "type theorem concerning biholomorphic equivalence",
      "docquier-grauert type theorem concerning biholomorphic",
      "big euclidean domains",
      "open neighbourhoods"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}