Results in Mathematics

, Volume 68, Issue 3–4, pp 455–499 | Cite as

Hyper-ideal Circle Patterns with Cone Singularities

  • Nikolay Dimitrov


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.


Hyper-ideal circle pattern cell complex hyper-ideal tetrahedron hyperbolic volume variational principle 

Mathematics Subject Classification

52C26 52A55 57M50 52C25 


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© Springer Basel 2015

Authors and Affiliations

  1. 1.Insitut für Mathematik MA 8-4Technische Universität BerlinBerlinGermany

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