On the Reverse Loomis-Whitney Inequality

The present paper deals with the problem of computing (or at least estimating) the LW-number λ(n), i.e., the supremum of all numbers c such that for each convex body K in R^n there exists an isometry g so that the volume of K is larger than the product of the n-1 volume of the orthogonal projections of gK onto the coordinate hyperplanes. Any such inequality can be regarded as a reverse to the well-known classical Loomis–Whitney inequality. We present various results on such reverse Loomis–Whitney inequalities. In particular, we prove some structural results, give bounds on λ(n) and deal with the problem of actually computing the LW-constant of a rational polytope.