Groups, Geometry, and Dynamics
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Published online: 2008-12-31
Entropy and isoperimetry for linear and non-linear group actionsMisha Gromov (1) Institut des Hautes Études 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