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Conformal Geometry and Dynamics

Published by the American Mathematical Society since 1997, the purpose of this electronic-only journal is to provide a forum for mathematical work in related fields broadly described as conformal geometry and dynamics. All articles are freely available to all readers and with no publishing fees for authors.

ISSN 1088-4173

The 2020 MCQ for Conformal Geometry and Dynamics is 0.49.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


An explicit counterexample to the equivariant $K=2$ conjecture
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by Yohei Komori and Charles A. Matthews
Conform. Geom. Dyn. 10 (2006), 184-196
Published electronically: August 24, 2006


We construct an explicit example of a geometrically finite Kleinian group $G$ with invariant component $\Omega$ in the Riemann sphere $\textbf {\hat {C}}$ such that any quasiconformal map from $\Omega$ to the boundary of the convex hull of $\textbf {\hat {C}} - \Omega$ in $\textbf {H^3}$ which extends to the identity map on their common boundary in $\textbf {\hat {C}}$, and which is equivariant under the group of Möbius transformations preserving $\Omega$, must have maximal dilatation $K > 2.002$.
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Bibliographic Information
  • Yohei Komori
  • Affiliation: Department of Mathematics, Osaka City University, Osaka 558-8585, Japan
  • Email:
  • Charles A. Matthews
  • Affiliation: Department of Mathematics, Southeastern Oklahoma State University, Durant, Oklahoma 74701
  • Email:
  • Received by editor(s): April 20, 2006
  • Published electronically: August 24, 2006
  • © Copyright 2006 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Conform. Geom. Dyn. 10 (2006), 184-196
  • MSC (2000): Primary 30F40, 30F60, 32G15, 57M50
  • DOI:
  • MathSciNet review: 2261047