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...
| Authors: | , |
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| Format: | article |
| Publication Date: | 2021 |
| Country: | España |
| Institution: | Universidad Complutense de Madrid (UCM) |
| Repository: | Docta Complutense |
| Language: | English |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/129084 |
| Online Access: | https://hdl.handle.net/20.500.14352/129084 |
| Access Level: | Open access |
| Keyword: | Bounded local geometry Cheeger isoperimetric constant Gromov hyperbolicity Bounded local geometry Pole Gromov hyperbolicity Pole Geometría diferencial 1204.04 Geometría Diferencial |
| Summary: | 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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