Variational principles for circle patterns and Koebe's theorem
arXiv:math/0203250
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.
33 pages, 12 figures, Appendix. Revised version. Appendix on cellular surfaces removed, references added and removed, typos corrected, a few minor changes