Coulhon Saloff-Coste isoperimetric inequalities for finitely generated groups
Group Theory
2022-11-08 v1 Metric Geometry
Abstract
We prove an inequality, valid on any finitely generated group with a fixed finite symmetric generating set, involving the growth of successive balls, and the average length of an element in a ball. It generalizes recent improvements of the Coulhon Saloff-Coste inequality. We reformulate the inequality in terms of the F{\o}lner function; in the case the finitely generated group is amenable with exponential growth, this allows us to express the best possible (outer) constant in the Coulhon Saloff-Coste isoperimetric inequality with the help of a formula involving the growth rate and the asymptotic behavior of the F{\o}lner function.
Keywords
Cite
@article{arxiv.2211.03227,
title = {Coulhon Saloff-Coste isoperimetric inequalities for finitely generated groups},
author = {Christophe Pittet and Bogdan Stankov},
journal= {arXiv preprint arXiv:2211.03227},
year = {2022}
}
Comments
13 pages