{
  "id": "0909.1041",
  "version": "v1",
  "published": "2009-09-05T17:44:31.000Z",
  "updated": "2009-09-05T17:44:31.000Z",
  "title": "The Kobayashi metric, extremal discs, and biholomorphic mappings",
  "authors": [
    "Steven G. Krantz"
  ],
  "categories": [
    "math.CV"
  ],
  "abstract": "We study extremal discs for the Kobayashi metric. Inspired by work of Lempert on strongly convex domains, we present results on strongly pseudoconvex domains. We also consider a useful biholomorphic invariant, inspired by the Kobayashi (and Carath\\'{e}odory) metric, and prove several new results about biholomorphic equivalence of domains. Some useful results about automorphism groups of complex domains are also established.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-09-05T17:44:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "32E05",
      "32H02",
      "32T27",
      "32T05"
    ],
    "keywords": [
      "kobayashi metric",
      "biholomorphic mappings",
      "study extremal discs",
      "biholomorphic equivalence",
      "strongly convex domains"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0909.1041K"
    }
  }
}