An L p-Functional Busemann–Petty Centroid Inequality

The L-busemann-petty Centroid Inequality

The ratio between the volume of the p-centroid body of a convex body K in Rn and the volume of K attains its minimum value if and only if K is an origin symmetric ellipsoid. This result, the Lp-Busemann-Petty centroid inequality, was recently proved by Lutwak, Yang and Zhang. In this paper we show that all the intrinsic volumes of the p-centroid body of K are convex functions of a time-like par...

On the Reverse L-busemann-petty Centroid Inequality

The volume of the Lp-centroid body of a convex body K ⊂ Rd is a convex function of a time-like parameter when each chord of K parallel to a fixed direction moves with constant speed. This fact is used to study extrema of some affine invariant functionals involving the volume of the Lp-centroid body and related to classical open problems like the slicing problem. Some variants of the Lp-Busemann...

An Inequality for P-orthogonal Sums in Non-commutative L P

We give an alternate proof of one of the inequalities proved recently for martingales (=sums of martingale differences) in a non-commutative L p-space, with 1 < p < ∞, by Q. Xu and the author. This new approach is restricted to p an even integer, but it yields a constant which is O(p) when p → ∞ and it applies to a much more general kind of sums which we call p-orthogonal. We use mainly combina...

A NOTE ON AN L p-BRUNN–MINKOWSKI INEQUALITY FOR CONVEX MEASURES IN THE UNCONDITIONAL CASE

A stability result for mean width of L p - centroid bodies

We give a different proof of a recent result of Klartag [12] concerning the concentration of the volume of a convex body within a thin Euclidean shell and proving a conjecture of Anttila, Ball and Perissinaki [1]. It is based on the study of the Lp-centroid bodies. We prove an almost isometric reverse Hölder inequality for their mean width and a refined form of a stability result.