Hyper-ideal circle patterns with cone singularities
type: Item
instance of: scholarly article
title: Hyper-ideal circle patterns with cone singularities
zbMATH Open document ID: 1330.52026
author: Nikolay Dimitrov
published in: Results in Mathematics
publication date: 2015-11-06T00:00:00Z
full work available at URL: https://arxiv.org/abs/1406.6741
review text: 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.
reviewed by: Sorin-Mihai Grad
Mathematics Subject Classification ID: 52C26
Mathematics Subject Classification ID: 52A55
Mathematics Subject Classification ID: 57M50
Mathematics Subject Classification ID: 52C25
zbMATH DE Number: 6505285
zbMATH Keywords: hyper-ideal circle pattern
zbMATH Keywords: cell complex
zbMATH Keywords: hyper-ideal tetrahedron
zbMATH Keywords: hyperbolic volume
zbMATH Keywords: variational principle
zbMATH Keywords: alternative proof
MaRDI profile type: Publication
OpenAlex ID: W2054257149
arXiv ID: 1406.6741
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DOI: 10.1007/S00025-015-0453-3
description: scientific article