Domains of discontinuity for almost-Fuchsian groups

• Verfasst von: Sanders, Andrew [VerfasserIn]
• Titel: Domains of discontinuity for almost-Fuchsian groups
• Verf.angabe: Andrew Sanders
• Umfang: 18 S.
• Fussnoten: Article electronically published on August 18, 2016 ; Gesehen am 03.05.2018
• Titel Quelle: Enthalten in: American Mathematical Society: Transactions of the American Mathematical Society
• Jahr Quelle: 2017
• Band/Heft Quelle: 369(2017), 2, S. 1291-1308
• ISSN Quelle: 1088-6850
• DOI: doi:10.1090/tran/6789
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 1572608595

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 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.