Groups, Geometry, and Dynamics


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Volume 2, Issue 4, 2008, pp. 499–593
DOI: 10.4171/GGD/48

Published online: 2008-12-31

Entropy and isoperimetry for linear and non-linear group actions

Misha Gromov[1]

(1) Institut des Hautes √Čtudes Scientifiques, Bures-Sur-Yvette, France

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.

Keywords: Isoperimetric inequalities, amenable groups, group algebras, entropy

Gromov Misha: Entropy and isoperimetry for linear and non-linear group actions. Groups Geom. Dyn. 2 (2008), 499-593. doi: 10.4171/GGD/48