Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 44, 2019, 841-875

GEOMETRIC FINITENESS IN NEGATIVELY PINCHED HADAMARD MANIFOLDS

Michael Kapovich and Beibei Liu

UC Davis, Department of Mathematics
One Shields Avenue, Davis CA 95616, U.S.A.; kapovich 'at' math.ucdavis.edu

UC Davis, Department of Mathematics
One Shields Avenue, Davis CA 95616, U.S.A.; bxliu 'at' math.ucdavis.edu

Abstract. In this paper, we generalize Bonahon's characterization of geometrically infinite torsion-free discrete subgroups of PSL(2,C) to geometrically infinite discrete subgroups Γ of isometries of negatively pinched Hadamard manifolds X. We then generalize a theorem of Bishop to prove that every discrete geometrically infinite isometry subgroup Γ has a set of nonconical limit points with the cardinality of the continuum.

2010 Mathematics Subject Classification: Primary 20F65, 22E40, 53C20, 57N16.

Key words: Manifolds of negative curvature, discrete groups, geometric finiteness.

Reference to this article: M. Kapovich and B. Liu: Geometric finiteness in negatively pinched Hadamard manifolds. Ann. Acad. Sci. Fenn. Math. 44 (2019), 841-875.

Full document as PDF file

https://doi.org/10.5186/aasfm.2019.4444