We prove inequalities of isoperimetric type for groups acting on linear spaces and discuss related geometric and combinatorial problems, where we use the Boltzmann entropy to keep track of the cardinalities (and/or measures) of sets and of the dimensions of linear spaces.
Cite this article
Misha Gromov, Entropy and isoperimetry for linear and non-linear group actions. Groups Geom. Dyn. 2 (2008), no. 4, pp. 499–593DOI 10.4171/GGD/48