تقرير
Isoperimetry in Finitely Generated Groups
| العنوان: | Isoperimetry in Finitely Generated Groups |
|---|---|
| المؤلفون: | Correia, Bruno Luiz Santos, Troyanov, Marc |
| سنة النشر: | 2023 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Group Theory, 20F65, 20F69, 05C63 |
| الوصف: | We revisit the isoperimetric inequalities for finitely generated groups introduced and studied by N. Varopoulos, T. Coulhon and L. Saloff-Coste. Namely we show that a lower bound on the isoperimetric quotient of finite subsets in a finitely generated group is given by the $\U-$transform of its growth function, which is a variant of the Legendre transform. From this lower bound, we obtain some asymptotic estimates for the F{\o}lner function of the group. The paper also includes a discussion of some basic definitions from Geometric Group Theory and some basic properties of the $\U$-transform, including some computational techniques and its relation with the Legendre transform. Comment: 20 pages. The results in this paper refine those in arXiv:2110.15798 |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2308.15376 |
| رقم الأكسشن: | edsarx.2308.15376 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |