Nearly Fuchsian surface subgroups of finite covolume Kleinian groups

Jeremy Kahn; Alex Wright

doi:10.1215/00127094-2020-0049

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arXiv · 1809.07211

Nearly Fuchsian surface subgroups of finite covolume Kleinian groups

Jeremy Kahn·Alex Wright

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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.

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BibTeX RIS

Jeremy Kahn, Alex Wright. 2018-09-19. Nearly Fuchsian surface subgroups of finite covolume Kleinian groups. https://doi.org/10.1215/00127094-2020-0049

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