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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.


Intrinsic circle domains
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by Edward Crane
Conform. Geom. Dyn. 18 (2014), 65-84
Published electronically: May 1, 2014


Using quasiconformal mappings, we prove that any Riemann surface of finite connectivity and finite genus is conformally equivalent to an intrinsic circle domain $\Omega$ in a compact Riemann surface $S$. This means that each connected component $B$ of $S\setminus \Omega$ is either a point or a closed geometric disc with respect to the complete constant curvature conformal metric of the Riemann surface $(\Omega \cup B)$. Moreover, the pair $(\Omega , S)$ is unique up to conformal isomorphisms. We give a generalization to countably infinite connectivity. Finally, we show how one can compute numerical approximations to intrinsic circle domains using circle packings and conformal welding.
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Bibliographic Information
  • Edward Crane
  • Affiliation: Heilbronn Institute for Mathematical Research, School of Mathematics, University of Bristol, BS8 1TW, United Kingdom
  • Email:
  • Received by editor(s): March 27, 2013
  • Published electronically: May 1, 2014
  • © Copyright 2014 American Mathematical Society
  • Journal: Conform. Geom. Dyn. 18 (2014), 65-84
  • MSC (2010): Primary 30C20; Secondary 30F45, 30C30, 52C26
  • DOI:
  • MathSciNet review: 3199397