Luiz, BrunoCorreia, Bruno E.Troyanov, MarcSantos Correia, B2025-04-092025-04-082024-05-2410.1007/978-3-031-43510-2_12https://infoscience.epfl.ch/handle/20.500.14299/248949We 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 Følner 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.enFinitely generated groupsGrowthIsoperimetric inequalityFølner functionLambert W -function AMS Subject Classification 20F65, 20F69text::book/monograph::book part or chapter