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Variational principles for circle patterns and Koebe's theorem
Author(s):
Alexander
I.
Bobenko;
Boris
A.
Springborn
Journal:
Trans. Amer. Math. Soc.
356
(2004),
659-689.
MSC (2000):
Primary 52C26;
Secondary 53A30
Posted:
September 22, 2003
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Additional information
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:
10.1090/S0002-9947-03-03239-2
PII:
S 0002-9947(03)03239-2
Received by editor(s):
July 23, 2002
Posted:
September 22, 2003
Additional Notes:
The research was partially supported by the Sonderforschungsbereich 288
Copyright of article:
Copyright
2003,
American Mathematical Society
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