Variational principles for circle patterns and Koebe's theorem
Geometric Topology
2007-05-23 v2 Complex Variables
Metric Geometry
Abstract
We prove existence and uniqueness results for patterns of circles with prescribed intersection angles in 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 Verdi`ere's, Br"agger's and Rivin's functionals can be derived from ours.
Keywords
Cite
@article{arxiv.math/0203250,
title = {Variational principles for circle patterns and Koebe's theorem},
author = {Alexander I. Bobenko and Boris A. Springborn},
journal= {arXiv preprint arXiv:math/0203250},
year = {2007}
}
Comments
33 pages, 12 figures, Appendix. Revised version. Appendix on cellular surfaces removed, references added and removed, typos corrected, a few minor changes