3 papers
math.GT2026
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 commensurabi…
math.GT2026
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…
math.GT2025
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 HamenstÃ…