An Extremal Property of p-mean Width

Abstract

Several isoperimetric type inequalities for p-mean width of convex bodies in $$\mathbb {R}^n$$ are established. These inequalities show the interrelations among the p-mean width of a convex body in $$\mathbb {R}^n$$ , an isotropic measure on unit sphere, and the newly-introduced $$L_{r,s}$$ -pseudo-moment body of the given body in $$\mathbb {R}^n$$ . The equalities in these inequalities are all characterized by parallelotopes.