Isoperimetric Inequalities in Riemann Surfaces 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] Facultad de CC. Sociales de Talavera,Departamento de Matemáticas
[3] Universidad Carlos III de Madrid,undefined
来源：
The Journal of Geometric Analysis | 2021年 / 31卷
关键词：
Isoperimetric inequality; Cheeger isoperimetric constant; Riemann surface; Poincaré metric; Gromov hyperbolicity; Primary 53C21; 53C23; Secondary 58C40;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
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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页码：3583 / 3607
页数：24
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