On a Loomis-Whitney Type Inequality for Permutationally Invariant   Unconditional Convex Bodies
  For a permutationally invariant unconditional convex body K in R^n we define a finite sequence (K_j), j = 1, ..., n of projections of the body K to the space spanned by first j vectors of the standard basis of R^n. We prove that the sequence of volumes (|K_1|, ..., |K_n|) is log-concave. 
Piotr Nayar, Tomasz Tkocz
math.FA