{
  "id": "math/9812164",
  "version": "v1",
  "published": "1998-12-31T21:17:07.000Z",
  "updated": "1998-12-31T21:17:07.000Z",
  "title": "Holomorphic Removability of Julia Sets",
  "authors": [
    "Jeremy Kahn"
  ],
  "comment": "48 pages. 9 PostScript figures",
  "categories": [
    "math.DS",
    "math.CV"
  ],
  "abstract": "Let $f(z) = z^2 + c$ be a quadratic polynomial, with c in the Mandelbrot set. Assume further that both fixed points of f are repelling, and that f is not renormalizable. Then we prove that the Julia set J of f is holomorphically removable in the sense that every homeomorphism of the complex plane to itself that is conformal off of J is in fact conformal on the entire complex plane. As a corollary, we deduce that the Mandelbrot Set is locally connected at such c.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1998-12-31T21:17:07.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "julia set",
      "holomorphic removability",
      "mandelbrot set",
      "entire complex plane",
      "quadratic polynomial"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 48,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1998math.....12164K"
    }
  }
}