  Zhang's reverse affine isoperimetric inequality states that among all convex
bodies $K\subseteq\mathbb{R}^n$, the affine invariant quantity
$|K|^{n-1}|\Pi^*(K)|$ (where $\Pi^*(K)$ 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.
