It is a wellknown conjecture (or maybe just a question) that all hyperbolic groups are residually finite. What happens if we weaken the conclusion; in particular
Are all hyperbolic groups residually amenable?
What is known in this direction?
It is a wellknown conjecture (or maybe just a question) that all hyperbolic groups are residually finite. What happens if we weaken the conclusion; in particular Are all hyperbolic groups residually amenable? What is known in this direction? 


Proposition 7 of this paper establishes that every hyperbolic group is residually amenable iff every hyperbolic group is residually finite. 

