Isoperimetric Inequalities in Riemann Surfaces and Graphs
A celebrated theorem of Kanai states that quasi-isometries preserve isoperimetric inequalities between uniform Riemannian manifolds (with positive injectivity radius) and graphs. Our main result states that we can study the (Cheeger) isoperimetric inequality in a Riemann surface by using a graph rel...
| Autores: | , |
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| 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:20.500.14352/129071 |
| Acceso en línea: | https://hdl.handle.net/20.500.14352/129071 |
| Access Level: | acceso abierto |
| Palabra clave: | Cheeger isoperimetric constant Gromov hyperbolicity Isoperimetric inequality Poincaré metric Riemann surface Geometría diferencial 1204.04 Geometría Diferencial |
| Sumario: | A celebrated theorem of Kanai states that quasi-isometries preserve isoperimetric inequalities between uniform Riemannian manifolds (with positive injectivity radius) and graphs. Our main result states that we can study the (Cheeger) isoperimetric inequality in a Riemann surface by using a graph related to it, even if the surface has injectivity radius zero (this graph is inspired in Kanai’s graph, but it is different from it). We also present an application relating Gromov boundary and isoperimetric inequality. |
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