Martínez Pérez, AlvaroRodríguez García, José Manuel2022-07-202022-07-202021-06-26Martínez-Pérez, Á., & Rodríguez, J. M. (2021). A note on isoperimetric inequalities of Gromov hyperbolic manifolds and graphs. In Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas (Vol. 115, Issue 3). Springer Science and Business Media LLC.1579-1505https://hdl.handle.net/10016/35497We 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.10engCopyright © 2021, The Author(s)Atribución 3.0 EspañaCheeger Isoperimetric ConstantGromov HyperbolicityBounded Local GeometryPoleresearch articleMatemáticashttps://doi.org/10.1007/s13398-021-01096-2open access115410Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas115AR/0000030821