{
  "id": "1411.0600",
  "version": "v1",
  "published": "2014-11-03T18:45:48.000Z",
  "updated": "2014-11-03T18:45:48.000Z",
  "title": "A boundary Schwarz Lemma for holomorphic mappings between unit balls of different dimensions",
  "authors": [
    "Yang Liu",
    "Zhihua Chen",
    "Yifei Pan"
  ],
  "comment": "10 pages",
  "categories": [
    "math.CV"
  ],
  "abstract": "In this paper, we give a general boundary Schwarz lemma for holomorphic mappings between unit balls in any dimensions. It is proved that if the mapping $f\\in C^{1+\\alpha}$ at $z_0\\in \\partial \\mathbb B^n$ with $f(z_0)=w_0\\in \\partial \\mathbb B^N$ for any $n,N\\geq 1$, then the Jacobian matrix $J_f(z_0)$ maps the tangent space $T_{z_0}(\\partial \\mathbb B^n)$ to $T_{w_0}(\\partial \\mathbb B^N)$, and the holomorphic tangent space $T^{(1,0)}_{z_0}(\\partial \\mathbb B^n)$ to $T^{(1,0)}_{w_0}(\\partial \\mathbb B^N)$ as well.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-11-03T18:45:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "32H02",
      "30C80"
    ],
    "keywords": [
      "holomorphic mappings",
      "unit balls",
      "dimensions",
      "general boundary schwarz lemma",
      "holomorphic tangent space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}