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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.


Convergence in discrete Cauchy problems and applications to circle patterns
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by D. Matthes
Conform. Geom. Dyn. 9 (2005), 1-23
Published electronically: February 9, 2005


A lattice-discretization of analytic Cauchy problems in two dimensions is presented. It is proven that the discrete solutions converge to a smooth solution of the original problem as the mesh size $\varepsilon$ tends to zero. The convergence is in $C^\infty$ and the approximation error for arbitrary derivatives is quadratic in $\varepsilon$. In application, $C^\infty$-approximation of conformal maps by Schramm’s orthogonal circle patterns and lattices of cross-ratio minus one is shown.
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Bibliographic Information
  • D. Matthes
  • Affiliation: Institut für Mathematik, Technische Universität Berlin, Straße des 17.Juni 136, 10623 Berlin, Germany
  • Address at time of publication: Institut für Mathematik, Johannes Gutenberg Universität Mainz, Staudingerweg 9, 55128 Mainz, Germany
  • MR Author ID: 722279
  • Email:
  • Received by editor(s): March 19, 2004
  • Received by editor(s) in revised form: November 16, 2004
  • Published electronically: February 9, 2005
  • Additional Notes: Supported by the SFB 288 “Differential Geometry and Quantum Physics” of the Deutsche Forschungsgemeinschaft
  • © Copyright 2005 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Conform. Geom. Dyn. 9 (2005), 1-23
  • MSC (2000): Primary 30G25; Secondary 35A10, 52C15
  • DOI:
  • MathSciNet review: 2133803