On the classification of discrete conformal structures on surfaces
Differential Geometry
2024-08-20 v3
Abstract
Glickenstein \cite{Glickenstein} and Glickenstein-Thomas \cite{GT} introduced the discrete conformal structures on surfaces in an axiomatic approach and studied its classification. In this paper, we give a full classification of the discrete conformal structures on surfaces, which completes Glickenstein-Thomas' classification. As a result, we find some new classes of discrete conformal structures on surfaces, including some of the generalized circle packing metrics introduced by Guo-Luo \cite{GL2}. The relationships between the discrete conformal structures on surfaces and the 3-dimensional hyperbolic geometry are also discussed.
Cite
@article{arxiv.2307.13223,
title = {On the classification of discrete conformal structures on surfaces},
author = {Xu Xu and Chao Zheng},
journal= {arXiv preprint arXiv:2307.13223},
year = {2024}
}