Herein we study p-parabolicity on graphs. We prove that if a uniform graph satisfies the
(Cheeger) isoperimetric inequality, then it is non-p-parabolic for every 1< p<∞. Moreover …

In this paper, we study the relationship of hyperbolicity and (Cheeger) isoperimetric
inequality in the context of Riemannian manifolds and graphs. We characterize the …

Kanai proved the stability under quasi‐isometries of numerous global properties (including
existence of Green's function, ie, non‐parabolicity) between Riemannian manifolds of …

We study in this paper the relationship of isoperimetric inequality and hyperbolicity for
graphs and Riemannian manifolds. We obtain a characterization of graphs and Riemannian …

A celebrated theorem of Kanai states that quasi-isometries preserve isoperimetric
inequalities between uniform Riemannian manifolds (with positive injectivity radius) and …

Kanai proved powerful results on the stability under quasi-isometries of numerous global
properties (including the volume growth rate) between non-bordered Riemannian manifolds …

Kanai proved that quasi-isometries between Riemannian manifolds with bounded geometry
preserve many global properties, including the existence of Green's function, ie, non …