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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.


Bounded outdegree and extremal length on discrete Riemann surfaces
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by William E. Wood
Conform. Geom. Dyn. 14 (2010), 194-201
Published electronically: August 2, 2010


Let $T$ be a triangulation of a Riemann surface. We show that the $1$-skeleton of $T$ may be oriented so that there is a global bound on the outdegree of the vertices. Our application is to construct extremal metrics on triangulations formed from $T$ by attaching new edges and vertices and subdividing its faces. Such refinements provide a mechanism of convergence of the discrete triangulation to the classical surface. We will prove a bound on the distortion of the discrete extremal lengths of path families on $T$ under the refinement process. Our bound will depend only on the refinement and not on $T$. In particular, the result does not require bounded degree.
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Bibliographic Information
  • William E. Wood
  • Affiliation: Department of Mathematics and Computer Science, 1600 Washington Avenue, Hendrix College, Conway, Arkansas 72032
  • Email:
  • Received by editor(s): September 1, 2009
  • Published electronically: August 2, 2010
  • © Copyright 2010 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Conform. Geom. Dyn. 14 (2010), 194-201
  • MSC (2000): Primary 52C26; Secondary 53A30, 05C10, 57M15
  • DOI:
  • MathSciNet review: 2672225