  In this paper we study the relationship of hyperbolicity and (Cheeger)
isoperimetric inequality in the context of Riemannian manifolds and graphs. We
characterize the hyperbolic manifolds and graphs (with bounded local geometry)
verifying this isoperimetric inequality, in terms of their Gromov boundary
improving similar results from a previous work. In particular, we prove that
having a pole is a necessary condition and, therefore, it can be removed as
hypothesis.
