1 citations · 1 across the 6 of their papers we have counts for
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Discrete uniformization of polyhedral surfaces
Feng Luo, Yanwen Luo, Zhenghao Rao +1
The main result of the paper shows that each connected polyhedral surface with a hyperbolic background metric, or a Euclidean background metric with uniformly bounded circumdisk ra…
Counting surface subgroups in cusped hyperbolic 3-manifolds
Xiaolong Hans Han, Zhenghao Rao, Jia Wan
Let be a finite-volume, noncompact hyperbolic 3-manifold. We show that the number of quasi-Fuchsian surface subgroups of (up to conjugacy and commensurabili…
A Rigidity Theorem for Convex Sets in Hyperbolic 3-Space
Feng Luo, Yanwen Luo, Zhenghao Rao
Pogorelov's rigidity theorem states that a compact convex body in the hyperbolic 3-space is determined up to isometry by the intrinsic path metric on its boundary. The main result…
Surface Subgroups for Cocompact Lattices of Isometries of
Jeremy Kahn, Zhenghao Rao
We prove the existence of surface subgroups within any cocompact lattice in for . This result addresses the cases missing from the work of Hamenstäd…
Subgroups of Genus-2 Quasi-Fuchsian groups and Cocompact Kleinian Groups
Zhenghao Rao
In this paper, we want to control the geometry of some surface subgroups of a cocompact Kleinian group. More precisely, provided any genus-2 quasi-Fuchsian group and cocompact…
Spaces of Geodesic Triangulations Are Cells
Yanwen Luo, Zhenghao Rao, Tianqi Wu +1
It has been shown that spaces of geodesic triangulations of closed negatively curved surfaces are contractible. Here we prove that these spaces are homeomorphic to Euclidean spaces…