%0 Journal Article
%A Martínez Pérez, Álvaro
%A Rodríguez, José M.
%T A note on isoperimetric inequalities of Gromov hyperbolic manifolds and graphs
%D 2021
%@ 1578-7303
%@ 1579-1505
%U https://hdl.handle.net/20.500.14352/129084
%X 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 manifolds (with bounded local geometry) satisfying the (Cheeger) 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 to have isoperimetric inequality and, therefore, it can be removed as hypothesis.
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