Nearly Fuchsian surface subgroups of finite covolume Kleinian groups

Abstract

Let Gamma < PSL_2(C) be discrete, cofinite volume, and noncocompact. We prove that for all K > 1, there is a subgroup H < Gamma that is K-quasiconformally conjugate to a discrete cocompact subgroup of PSL_2(R). Along with previous work of Kahn and Markovic, this proves that every finite covolume Kleinian group has a nearly Fuchsian surface subgroup.

v2: Final prepublication version

References in corpus (4)

• Initialization of lattice Boltzmann models with the help of the numerical Chapman-Enskog expansion
• Ubiquitous quasi-Fuchsian surfaces in cusped hyperbolic 3-manifolds
• Finite-volume Hyperbolic 3-Manifolds contain immersed Quasi-Fuchsian surfaces
• Quasi-Fuchsian Surfaces In Hyperbolic Link Complements

Cited by in corpus (4)

• Ubiquitous quasi-Fuchsian surfaces in cusped hyperbolic 3-manifolds
• Virtual Domination of 3-manifolds III
• Counting essential minimal surfaces in closed negatively curved n-manifolds
• Thin subgroups isomorphic to Gromov--Piatetski-Shapiro lattices