Geometric finiteness in negatively pinched Hadamard manifolds
Group Theory
2018-12-24 v3 Differential Geometry
Geometric Topology
Abstract
In this paper, we generalize Bonahon's characterization of geometrically infinite torsion-free discrete subgroups of PSL(2, ) to geometrically infinite discrete subgroups of isometries of negatively pinched Hadamard manifolds . We then generalize a theorem of Bishop to prove that every discrete geometrically infinite isometry subgroup has a set of nonconical limit points with the cardinality of the continuum.
Keywords
Cite
@article{arxiv.1801.08239,
title = {Geometric finiteness in negatively pinched Hadamard manifolds},
author = {Michael Kapovich and Beibei Liu},
journal= {arXiv preprint arXiv:1801.08239},
year = {2018}
}
Comments
We 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