A note on isoperimetric inequalities of Gromov hyperbolic manifolds and graphs
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Published:2021-06-26
Issue:3
Volume:115
Page:
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ISSN:1578-7303
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Container-title:Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas
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language:en
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Short-container-title:RACSAM
Author:
Martínez-Pérez ÁlvaroORCID, Rodríguez José M.ORCID
Abstract
AbstractWe 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.
Funder
Ministerio de Ciencia, Innovación y Universidades Agencia Estatal de Investigación Comunidad de Madrid
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Computational Mathematics,Geometry and Topology,Algebra and Number Theory,Analysis
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