An almost-Fuchsian group is a quasi-Fuchsian group such that the quotient hyperbolic manifold contains a closed incompressible minimal surface with principal curvatures contained in (-1,1) . We show that the domain of discontinuity of an almost-Fuchsian group contains many balls of a fixed spherical radius in the visual boundary of hyperbolic 3-space. This yields a necessary condition for a quasi-Fuchsian group to be almost-Fuchsian which involves only conformal geometry. As an application, we prove that there are no doubly-degenerate geometric limits of almost-Fuchsian groups.
SEEK ID: https://publications.h-its.org/publications/958
DOI: 10.1090/tran/6789
Research Groups: Groups and Geometry
Publication type: Journal
Journal: Transactions of the American Mathematical Society
Citation: Trans. Amer. Math. Soc. 369(2):1291-1308
Date Published: 1st Feb 2017
URL: https://www.ams.org/journals/tran/2017-369-02/S0002-9947-2016-06789-6/
Registered Mode: imported from a bibtex file
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Created: 30th Jan 2020 at 09:39
Last updated: 5th Mar 2024 at 21:24
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