10 papers · 1 filter
Combinatorial Yamabe flow on infinitely triangulated hyperbolic surfaces
Yuerong Bian, Xu Xu
We study the combinatorial Yamabe flow on infinitely triangulated surfaces with piecewise hyperbolic metrics. Under the assumptions of uniformly bounded vertex degree and -unifo…
Infinite rigidity of inversive distance circle packings in the Poincaré disk
Yanwen Luo, Xu Xu, Chao Zheng
The maximum principle for hyperbolic inversive distance circle packings on polyhedral surfaces is established,which unifies and generalizes existing maximum principles for various…
Discrete conformal structures on surfaces with boundary (III) -- Deformation
Xu Xu, Chao Zheng
The present work constitutes the third installment in a series of investigations devoted to discrete conformal structures on surfaces with boundary. In our preceding works \cite{X-…
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…
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…
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…