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math.DG2024
Discrete conformal structures on surfaces with boundary (II) -- Rigidity and Existence
Xu Xu, Chao Zheng
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 struc…
math.DG2024
A discrete uniformization theorem for decorated piecewise hyperbolic metrics on surfaces
Xu Xu, Chao Zheng
In this paper, we study a natural discretization of the smooth Gaussian curvature on surfaces. A discrete uniformization theorem is established for this discrete Gaussian curvature…
math.DG2024
Discrete conformal structures on surfaces with boundary (I) -- Classification
Xu Xu, Chao Zheng
In this paper, we introduce the discrete conformal structures on surfaces with boundary in an axiomatic approach, which ensures that the Poincaré dual of an ideally triangulated su…