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Hyper-ideal Circle Patterns with Cone Singularities

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Abstract

The main objective of this study is to explore how hyper-ideal circle patterns can be reconstructed from given combinatorial angle data. More precisely, we focus on the existence, uniqueness and construction of hyper-ideal circle patterns with prescribed combinatorics and intersection angles between adjacent circles. In essence, we propose a new proof of the already existing results from Jean-Marc Schlenker’s work on the topic. Our attempt is to develop a slightly different approach that is potentially more suitable for applications and thus leading to a more direct convex variational principle than Schlenker’s.

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  1. Insitut für Mathematik MA 8-4, Technische Universität Berlin, Straße des 17. Juni 136, 10623, Berlin, Germany

    Nikolay Dimitrov

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  1. Nikolay Dimitrov
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Correspondence to Nikolay Dimitrov.

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Dimitrov, N. Hyper-ideal Circle Patterns with Cone Singularities. Results. Math. 68, 455–499 (2015). https://doi.org/10.1007/s00025-015-0453-3

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