Hyper-ideal circle patterns with cone singularities
The author proposes a new proof to a result on how hyper-ideal circle patterns can be reconstructed from given combinatorial angle data from [\textit{J.-M. Schlenker}, Discrete Comput. Geom. 40, No. 1, 47--102 (2008; Zbl 1191.52013)]. More precisely, the focus of the paper is on the existence, uniqueness and construction of hyper-ideal circle patterns with prescribed combinatorics and intersection angles between adjacent circles. The importance of the new approach resides in the fact that is potentially more suitable for applications than the original one and thus can lead to a more direct convex variational principle. Necessary and sufficient conditions for the existence of circle patterns are provided as well.
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