Non-amenability and visual Gromov hyperbolic spaces
arXiv:1505.04662
Abstract
We prove that a uniformly coarsely proper hyperbolic cone over a bounded metric space consisting of a finite union of uniformly coarsely connected components each containing at least two points is non-amenable and apply this to visual Gromov hyperbolic spaces.
To appear in Groups Geom. Dyn. 11 (2017)