Two Characterizations of Geometrically Infinite Actions on Gromov Hyperbolic Spaces
Abstract
We provide two new characterizations of geometrically infinite actions on Gromov hyperbolic spaces: one in terms of the existence of escaping geodesics, and the other via the presence of uncountably many non-conical limit points. These results extend corresponding theorems of Bonahon, Bishop, and Kapovich--Liu from the settings of Kleinian groups and pinched negatively curved manifolds to discrete groups acting properly on proper Gromov hyperbolic spaces.
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