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.
Cite this article
Juhani Koivisto, Non-amenability and visual Gromov hyperbolic spaces. Groups Geom. Dyn. 11 (2017), no. 2, pp. 685–704DOI 10.4171/GGD/412