论文标题
有限生成的组
Coulhon Saloff-Coste isoperimetric inequalities for finitely generated groups
论文作者
论文摘要
我们证明了一种不等式，在任何有限生成的基团中有效的有限对称生成集，涉及连续球的生长以及球中元素的平均长度。它概括了Coulhon Saloff-Coste不平等现象的最新改善。我们从Følner功能方面重新制定了不平等；在这种情况下，有限生成的组可以随着指数增长而适应，这使我们能够在涉及Følner功能的增长率和渐近行为的公式的帮助下，表达库尔恩·萨洛夫 - 苏洛夫 - 塞氏等等的最佳（外部）常数。
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 Følner 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 Følner function.
