Abstract
Zhang’s reverse affine isoperimetric inequality states that among all convex bodies \(K\subseteq \mathbb R^n\), the affine invariant quantity |K|n−1| Π∗(K)| (where Π∗(K) denotes the polar projection body of K) is minimized if and only if K is a simplex. In this paper we prove an extension of Zhang’s inequality in the setting of integrable log-concave functions, characterizing also the equality cases.
The first and second authors are partially supported by MINECO Project MTM2016-77710-P, DGA E26_17R and IUMA, and the third author is partially supported by Fundación Séneca, Programme in Support of Excellence Groups of the Región de Murcia, Project 19901/GERM/15, and by MINECO Project MTM2015-63699-P and MICINN Project PGC2018-094215-B-I00.
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Alonso-Gutiérrez, D., Bernués, J., González Merino, B. (2020). Zhang’s Inequality for Log-Concave Functions. In: Klartag, B., Milman, E. (eds) Geometric Aspects of Functional Analysis. Lecture Notes in Mathematics, vol 2256. Springer, Cham. https://doi.org/10.1007/978-3-030-36020-7_2
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DOI: https://doi.org/10.1007/978-3-030-36020-7_2
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