Domains of discontinuity for almost-Fuchsian groups - Sanders, Andrew (Transactions of the American Mathematical Society, 2017)
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 We show that the domain of discontinuity of an almost-Fuchsian group contains many balls of a fixed spherical radius in 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.