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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
DOI: https://doi.org/10.1090/S0002-9947-03-03239-2
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
MR Author ID: 191410
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

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