Domains of discontinuity for almost-Fuchsian groups


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.


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


Registered Mode: imported from a bibtex file

Author: Andrew Sanders

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Sanders, A. (2016). Domains of discontinuity for almost-Fuchsian groups. In Transactions of the American Mathematical Society (Vol. 369, Issue 2, pp. 1291–1308). American Mathematical Society (AMS).

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Created: 30th Jan 2020 at 09:39

Last updated: 5th Mar 2024 at 21:24

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