Inequalities for Dual Affine Quermassintegrals

The setting for this paper is n-dimensional Euclidean space Rn. Let n denote the set of convex bodies (compact, convex subsets with nonempty interiors) and n o denote the subset of n that consists of convex bodies with the origin in their interiors. Denote by voli(K | ξ) the i-dimensional volume of the orthogonal projection of K onto an idimensional subspace ξ ⊂Rn. Affine quermassintegrals are important geometric invariants related to the projection of convex body. These quermassintegrals were introduced by Lutwak [7], and can be defined by letting Φ0(K)=V(K),Φn(K)= kn, and for 0 < i < n,