Variational principles for circle patterns and Koebe's theorem

Details Variational principles for circle patterns and Koebe's theorem Variational principles for circle patterns and Koebe's theorem

2002-03-25

arxiv.org/abs/math/0203250v2

Trans. Amer. Math. Soc. 356 (2004), 659-689.

Mathematics

Geometric Topology

33 pages, 12 figures, Appendix. Revised version. Appendix on cellular surfaces removed, references added and removed, typos co

Scientific paper

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.

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