Equality cases in Janson’s higher-order inequality

Characterize all full-dimensional convex bodies attaining equality in Janson’s inequality V(-Δ_{n-1}K[n-1],ι_1K,…,ι_{n-1}K)≤((n!)^n/(n^2-n)!)|K|^{n-1}, and determine whether simplices are the only nontrivial extremizers.

Background

The paper derives Janson’s inequality by applying Schneider’s inequality and taking a limit. The limiting argument establishes the bound but does not provide information about equality.

The authors explicitly identify the classification of equality cases as unresolved, even though the inequality itself is used to verify a low-dimensional case of the refined higher-order Godbersen conjecture.