A note on isoperimetric inequalities of Gromov hyperbolic manifolds and graphs

被引：0
作者：
Álvaro Martínez-Pérez
José M. Rodríguez
机构：
[1] Universidad de Castilla-La Mancha,Departamento de Análisis Económico y Finanzas
[2] Universidad Carlos III de Madrid,Departamento de Matemáticas
来源：
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas | 2021年 / 115卷
关键词：
Cheeger isoperimetric constant; Gromov hyperbolicity; Bounded local geometry; Pole; 53C21; 53C23; 58C40;
D O I：
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学科分类号：
摘要：
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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