Two Characterizations of Geometrically Infinite Actions on Gromov Hyperbolic Spaces
Chaodong Yang, Wenyuan Yang
TL;DR
This paper introduces two new characterizations of geometrically infinite actions on Gromov hyperbolic spaces, extending classical theorems from Kleinian groups to a broader setting.
Contribution
It provides novel criteria based on escaping geodesics and non-conical limit points for understanding infinite actions in Gromov hyperbolic spaces.
Findings
Characterization via escaping geodesics
Presence of uncountably many non-conical limit points
Extends classical results to 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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