6 papers · 1 filter
Characterizations of infinite circle patterns and convex polyhedra in hyperbolic 3-space
Huabin Ge, Longsong Jia, Hao Yu +1
Since Thurston pioneered the connection between circle packing (abbr. CP) and three-dimensional geometric topology, the characterization of CPs and hyperbolic polyhedra has become…
Characterization of Infinite Ideal Polyhedra in Hyperbolic 3-Space via Combinatorial Ricci Flow
Huabin Ge, Bobo Hua, Hao Yu +1
In his seminal work \cite{Ri96}, Rivin characterized finite ideal polyhedra in three-dimensional hyperbolic space. However, the characterization of infinite ideal polyhedra, as pro…
Infinite Ideal Polyhedra in Hyperbolic 3-Space: Existence and Rigidity
Huabin Ge, Hao Yu, Puchun Zhou
In the seminal work [27], Rivin obtained a complete characterization of finite ideal polyhedra in hyperbolic 3-space by the exterior dihedral angles. Since then,the characterizatio…
Angle structures on pseudo 3-manifolds
Huabin Ge, Longsong Jia, Faze Zhang
It is still not known whether a hyperbolic 3-manifold admits an angle structure or not. We consider angle structures with area-curvature on triangulated pseudo 3-manifolds M in thi…
The polyhedral decomposition of cusped hyperbolic -manifolds with totally geodesic boundary
Ge Huabin, Jia Longsong, Zhang Faze
Let be a volume finite non-compact complete hyperbolic -manifold with totally geodesic boundary. We show that there exists a polyhedral decomposition of such that each c…
Angle structure on general hyperbolic 3-manifolds
Ge Huabin, Jia Longsong, Zhang Faze
Let be a non-compact hyperbolic -manifold with finite volume and totally geodesic boundary components. By subdividing mixed ideal polyhedral decompositions of , under som…