Discrete uniformization of finite branched covers over the Riemann sphere via hyper-ideal circle patterns
Metric Geometry
2017-08-25 v1 Computational Geometry
Differential Geometry
Geometric Topology
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.
Keywords
Cite
@article{arxiv.1510.04053,
title = {Discrete uniformization of finite branched covers over the Riemann sphere via hyper-ideal circle patterns},
author = {Alexander Bobenko and Nikolay Dimitrov and Stefan Sechelmann},
journal= {arXiv preprint arXiv:1510.04053},
year = {2017}
}
Comments
43 pages, 10 figures