5 papers · 1 filter
Deformation of discrete conformal structures on surfaces
Xu Xu
Glickenstein introduced the discrete conformal structures on polyhedral surfaces in an axiomatic approach from Riemannian geometry perspective. It includes Thurston's circle packin…
A discrete uniformization theorem for decorated piecewise Euclidean metrics on surfaces, II
Xu Xu, Chao Zheng
In this paper, we study a natural discretization of the smooth Gaussian curvature on surfaces, which is defined as the quotient of the angle defect and the area of a geodesic disk…
A discrete uniformization theorem for decorated piecewise Euclidean metrics on surfaces
Xu Xu, Chao Zheng
In this paper, we introduce a new discretization of the Gaussian curvature on surfaces, which is defined as the quotient of the angle defect and the area of some dual cell of a wei…
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…
Rigidity and deformation of generalized 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 sphere packings on 3-dimensional manifolds with boundary. Then…