Variational principles for circle patterns and Koebe’s theorem
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- by Alexander I. Bobenko and Boris A. Springborn PDF
- Trans. Amer. Math. Soc. 356 (2004), 659-689 Request permission
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.References
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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
- © Copyright 2003 American Mathematical Society
- 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
- MathSciNet review: 2022715