Volume Inequalities for Isotropic Measures

Mathematics – Metric Geometry

Scientific paper

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10 pages, to appear in American Journal of Mathematics

Scientific paper

A direct approach to Ball's simplex inequality is presented. This approach,
which does not use the Brascamp-Lieb inequality, also gives Barthe's
characterization of the simplex for Ball's inequality and extends it from
discrete to arbitrary measures. It also yields the dual inequality, along with
equality conditions, and it does both for arbitrary measures.

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