Various results are proved giving lower bounds for the mth intrinsic volume
Vmβ(K), m=1,β¦,nβ1, of a compact convex set K in Rn, in
terms of the mth intrinsic volumes of its projections on the coordinate
hyperplanes (or its intersections with the coordinate hyperplanes). The bounds
are sharp when m=1 and m=nβ1. These are reverse (or dual, respectively)
forms of the Loomis-Whitney inequality and versions of it that apply to
intrinsic volumes. For the intrinsic volume V1β(K), which corresponds to mean
width, the inequality obtained confirms a conjecture of Betke and McMullen made
in 1983