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- W4386302958 abstract "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." @default.
- W4386302958 created "2023-08-31" @default.
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- W4386302958 date "2023-08-29" @default.
- W4386302958 modified "2023-10-14" @default.
- W4386302958 title "Isoperimetry in Finitely Generated Groups" @default.
- W4386302958 doi "https://doi.org/10.48550/arxiv.2308.15376" @default.
- W4386302958 hasPublicationYear "2023" @default.
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