Two Characterizations of Geometrically Infinite Actions on Gromov Hyperbolic Spaces
Group Theory
2026-04-16 v2
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.
Keywords
Cite
@article{arxiv.2602.19529,
title = {Two Characterizations of Geometrically Infinite Actions on Gromov Hyperbolic Spaces},
author = {Chaodong Yang and Wenyuan Yang},
journal= {arXiv preprint arXiv:2602.19529},
year = {2026}
}
Comments
22 pages, 4 figures