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Conformal Geometry and Dynamics

Published by the American Mathematical Society, the Conformal Geometry and Dynamics (ECGD) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4173

The 2020 MCQ for Conformal Geometry and Dynamics is 0.5.

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Extensions of homeomorphisms between limbs of the Mandelbrot set
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by Bodil Branner and Núria Fagella PDF
Conform. Geom. Dyn. 5 (2001), 100-139 Request permission


Using holomorphic surgery techniques, we construct a homeomorphism between a neighborhood of any limb without root point of the Mandelbrot set and a neighborhood of any other of equal denominator, in such a way that the limbs are mapped to each other. On the limbs, the homeomorphism coincides with that constructed in “Homeomorphisms between limbs of the Mandelbrot set” (J. Geom. Anal. 9 (1999), 327–390) which proves – without assuming local connectivity of the Mandelbrot set – that these maps are compatible with the embedding of the limbs in the plane. Outside the limbs, the constructed extension is quasi-conformal.
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Additional Information
  • Bodil Branner
  • Affiliation: Department of Mathematics, Technical University of Denmark, Building 303, DK-2800 Kongens Lyngby, Denmark
  • Email:
  • Núria Fagella
  • Affiliation: Departament de Matemàtica Aplicada i Anàlisi, Universitat de Barcelona, Gran Via 585, 08007 Barcelona, Spain
  • Email:
  • Received by editor(s): September 4, 2000
  • Received by editor(s) in revised form: May 10, 2001
  • Published electronically: October 18, 2001
  • Additional Notes: Partially supported by SNF Grant No. 9701387
    Partially supported by DGICYT Grant No. PB96-1153, BFM2000-0805-C02-01 and CIRIT 2000SGR-27
  • © Copyright 2001 American Mathematical Society
  • Journal: Conform. Geom. Dyn. 5 (2001), 100-139
  • MSC (2000): Primary 37F45; Secondary 37F10
  • DOI:
  • MathSciNet review: 1872159