Sfb 288 Differential Geometry and Quantum Physics

Abstract for Sfb Preprint No. 545

Variational principles for circle patterns and Koebe's theorem

Alexander I. Bobenko and Boris A. Springborn

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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