Discrete conformal structures on surfaces with boundary (II) -- Rigidity and Existence
Differential Geometry
2025-07-25 v3 Geometric Topology
Abstract
In \cite{X-Z DCS1}, we introduced discrete conformal structures on surfaces with boundary via an axiomatic framework, and provided a classification of such discrete conformal structures. The present work focuses on the rigidity and existence of these discrete conformal structures on surfaces with boundary. As a direct consequence, the results by Guo-Luo in \cite{GL2} and Guo in \cite{Guo}, which deal with the rigidity and existence of discrete conformal structures on surfaces with boundary, are extended to a very general context.
Cite
@article{arxiv.2407.19501,
title = {Discrete conformal structures on surfaces with boundary (II) -- Rigidity and Existence},
author = {Xu Xu and Chao Zheng},
journal= {arXiv preprint arXiv:2407.19501},
year = {2025}
}