Rodríguez García, José ManuelMartínez Pérez, Alvaro2021-05-132021-05-132018-08-01Martínez-Pérez, A., and Rodríguez, J. M. (2018). Cheeger isoperimetric constant of gromov hyperbolic manifolds and graphs. Communications in Contemporary Mathematics, 20(05), 17500500219-1997https://hdl.handle.net/10016/32615In 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. Furthermore, we characterize the trees with isoperimetric inequality (without any hypothesis). As an application of our results, we obtain the solvability of the Dirichlet problem at infinity for these Riemannian manifolds and graphs, and that the Martin boundary is homeomorphic to the Gromov boundary.24 p.eng© World Scientific PublishingGromov hyperbolicityCheeger isoperimetric constantBounded local geometryresearch articleMatemáticashttps://doi.org/10.1142/S021919971750050Xopen access17500505Communications in Contemporary Mathematics20AR/0000021691