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Zbl 0901.26010
Barthe, Franck
On a reverse form of the Brascamp-Lieb inequality. (English)
[J] Invent. Math. 134, No.2, 335-361 (1998). ISSN 0020-9910; ISSN 1432-1297/e

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.
[Franck Barthe (Marne la Vallée)]

MSC 2000:: *26D15 Inequalities for sums, series and integrals of real functions
52A40 Geometric inequalities, etc. (convex geometry)
52A38 Length, area, volume (convex geometry)

Keywords: Brascamp-Lieb inequalities; Monge-Ampère equation; converse inequalities; convex geometry; volume estimates; Brunn-Minkowski type inequalities

Cited in: Zbl 1208.26041 Zbl 1196.44003 Zbl 1117.52011 Zbl 1077.52004 Zbl 1052.52002

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