On a reverse form of the Brascamp-Lieb inequality. (English) Zbl 0901.26010

We derive a reverse form of the Brascamp-Lieb inequalities. The proof uses convex solutions of the Monge-Ampère equation and provides the Brascamp-Lieb inequalities and the converse inequalities altogether. We study equality cases for functions of one real variable. Next, we give applications to convex geometry: volume estimates, Brunn-Minkowski type inequalities.


26D15 Inequalities for sums, series and integrals
52A40 Inequalities and extremum problems involving convexity in convex geometry
52A38 Length, area, volume and convex sets (aspects of convex geometry)
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