Isoperimetric constants of metric probability spaces

Abstract: In this first talk we shall introduce four isoperimetric constants (the Cheeger constant, the Poincare constant, the exponential concentration constant and the first moment concentration constant) associated with a Borel probability measure on R^n and discuss their relation. We shall review classical results of Maz'ya, Cheeger, Gromov, V. Milman, Buser, Ledoux and others, as well as a theorem of E. Milman which establishes the equivalence of all four constants in the log-concave setting.

functional analysisoperator algebras

Audience: advanced learners

Functional analysis and operator algebras in Athens

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