A note on isoperimetric inequalities of Gromov hyperbolic manifolds and graphs

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 boundar...

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Detalles Bibliográficos
Autores: Martínez Pérez, Álvaro, Rodríguez, José M.
Tipo de recurso: artículo
Fecha de publicación:2021
País:España
Institución:Universidad Complutense de Madrid (UCM)
Repositorio:Docta Complutense
Idioma:inglés
OAI Identifier:oai:docta.ucm.es:20.500.14352/129084
Acceso en línea:https://hdl.handle.net/20.500.14352/129084
Access Level:acceso abierto
Palabra clave:Bounded local geometry
Cheeger isoperimetric constant Gromov hyperbolicity Bounded local geometry Pole
Gromov hyperbolicity
Pole
Geometría diferencial
1204.04 Geometría Diferencial
Descripción
Sumario: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.