Low dimensional sections versus projections of convex bodies

Abstract

The structure of low dimensional sections and projections of symmetric convex bodies is studied. For a symmetric convex bodyB ⊂ ℝ n , inequalities between the smallest diameter of rank l projections ofB and the largest in-radius ofm-dimensional sections ofB are established, for a wide range of sub-proportional dimensions. As an application it is shown that every bodyB in (isomorphic) l-position admits a well-bounded (√n, 1)-mixing operator.