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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Variational principles for circle patterns and Koebe's theorem


Authors: Alexander I. Bobenko and Boris A. Springborn
Journal: Trans. Amer. Math. Soc. 356 (2004), 659-689
MSC (2000): Primary 52C26; Secondary 53A30
Published electronically: September 22, 2003
MathSciNet review: 2022715
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Abstract: We prove existence and uniqueness results for patterns of circles with prescribed intersection angles on constant curvature surfaces. Our method is based on two new functionals--one for the Euclidean and one for the hyperbolic case. We show how Colin de Verdière's, Brägger's and Rivin's functionals can be derived from ours.


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Additional Information

Alexander I. Bobenko
Affiliation: Institut für Mathematik, MA 8-3, Technische Universität Berlin, Strasse des 17. Juni 136, 10623 Berlin, Germany
Email: bobenko@math.tu-berlin.de

Boris A. Springborn
Affiliation: Institut für Mathematik, MA 8-5, Technische Universität Berlin, Strasse des 17. Juni 136, 10623 Berlin, Germany
Email: springb@math.tu-berlin.de

DOI: http://dx.doi.org/10.1090/S0002-9947-03-03239-2
PII: S 0002-9947(03)03239-2
Received by editor(s): July 23, 2002
Published electronically: September 22, 2003
Additional Notes: The research was partially supported by the Sonderforschungsbereich 288
Article copyright: © Copyright 2003 American Mathematical Society