Convexity properties of sections of 1-symmetric bodies and Rademacher sums

Abstract

We establish a monotonicity-type property of volume of central hyperplane sections of the 1-symmetric convex bodies, with applications to chessboard cutting. We parallel this for projections with a new convexity-type property for Rademacher sums.

Final version. To appear in Proc. Amer. Math. Soc