Zhang's inequality for log-concave functions

2018/10/17 by Alonso-Gutiérrez, David, Bernués, Julio, Merino, Bernardo González · 3 citations
#FOS: Mathematics #Functional Analysis (math.FA) #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.1810.07507

Abstract

Zhang's reverse affine isoperimetric inequality states that among all convex bodies K⊆ℝⁿ, 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.

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