Geometric finiteness in negatively pinched Hadamard manifolds

Abstract

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

arXiv commentWe improved our results to any discrete geometrically infinite isometry subgroup of a negatively pinched Hadamard manifold, and we sharpened our main results to deal with limit sets of ends of the convex core

References in corpus (2)

• On the joint spectral radius for isometries of non-positively curved spaces and uniform growth
• Ping-pong in Hadamard manifolds

Cited by in corpus (1)

• Ping-pong in Hadamard manifolds