Domains of discontinuity for almost-Fuchsian Groups

Andrew Sanders

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arXiv · 1310.6412

Domains of discontinuity for almost-Fuchsian Groups

Andrew Sanders

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Abstract

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.

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Andrew Sanders. 2013-10-23. Domains of discontinuity for almost-Fuchsian Groups. https://arxiv.org/abs/1310.6412

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