Variational principles for circle patterns and Koebe's theorem

Alexander I. Bobenko; Boris A. Springborn

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Variational principles for circle patterns and Koebe's theorem

Alexander I. Bobenko·Boris A. Springborn

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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.

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Alexander I. Bobenko, Boris A. Springborn. 2002-06-03. Variational principles for circle patterns and Koebe's theorem. https://arxiv.org/abs/math/0203250

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