4 papers · 1 filter
Rigidity of generalized Thurston's sphere packings on 3-dimensional manifolds with boundary
Xu Xu, Chao Zheng
Motivated by Guo-Luo's generalized circle packings on surfaces with boundary \cite{GL2}, we introduce the generalized Thurston's sphere packings on 3-dimensional manifolds with bou…
A new proof for global rigidity of vertex scaling on polyhedral surfaces
Xu Xu, Chao Zheng
The vertex scaling for piecewise linear metrics on polyhedral surfaces was introduced by Luo, who proved the local rigidity by establishing a variational principle and conjectured…
Parameterized combinatorial curvatures and parameterized combinatorial curvature flows for discrete conformal structures on polyhedral surfaces
Xu Xu, Chao Zheng
Discrete conformal structure on polyhedral surfaces is a discrete analogue of the smooth conformal structure on surfaces that assigns discrete metrics by scalar functions defined o…
Parameterized discrete uniformization theorems and curvature flows for polyhedral surfaces, II
Xu Xu, Chao Zheng
This paper investigates the combinatorial -curvature for vertex scaling of piecewise hyperbolic metrics on polyhedral surfaces, which is a parameterized generalization of the cl…