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arXiv · 1510.04053

Discrete uniformization of finite branched covers over the Riemann sphere via hyper-ideal circle patterns

Alexander Bobenko·Nikolay Dimitrov·Stefan Sechelmann
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Abstract

With the help of hyper-ideal circle pattern theory, we have developed a discrete version of the classical uniformization theorems for surfaces represented as finite branched covers over the Riemann sphere as well as compact polyhedral surfaces with non-positive curvature. We show that in the case of such surfaces discrete uniformization via hyper-ideal circle patterns always exists and is unique. We also propose a numerical algorithm, utilizing convex optimization, that constructs the desired discrete uniformization.

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Alexander Bobenko, Nikolay Dimitrov, Stefan Sechelmann. 2015-10-14. Discrete uniformization of finite branched covers over the Riemann sphere via hyper-ideal circle patterns. https://arxiv.org/abs/1510.04053

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