Intersection bodies and dual mixed volumes

Inequalities for dual quermassintegrals of mixed intersection bodies

In this paper, we first introduce a new concept of dual quermassintegral sum function of two star bodies and establish Minkowski's type inequality for dual quermassintegral sum of mixed intersection bodies, which is a general form of the Minkowski inequality for mixed intersection bodies. Then, we give the Aleksandrov– Fenchel inequality and the Brunn–Minkowski inequality for mixed intersection...

Dual Mixed Volumes and the Slicing Problem

We develop a technique using dual mixed-volumes to study the isotropic constants of some classes of spaces. In particular, we recover, strengthen and generalize results of Ball and Junge concerning the isotropic constants of subspaces and quotients of Lp and related spaces. An extension of these results to negative values of p is also obtained, using generalized intersection-bodies. In particul...

Star Valuations and Dual Mixed Volumes

Since its creation by Brunn and Minkowski, what has become known as the Brunn Minkowski theory has provided powerful machinery to solve a broad variety of inverse problems with stereological data. The machinery of the Brunn Minkowski theory includes mixed volumes (of Minkowski), symmetrization techniques (such as those of Steiner and Blaschke), isoperimetric inequalities (such as the Brunn Mink...

the brunn-minkowski-type inequality

Volume difference inequalities for the projection and intersection bodies

In this paper, we introduce a new concept of volumes difference function of the projection and intersection bodies. Following this, we establish the Minkowski and Brunn-Minkowski inequalities for volumes difference function of the projection and intersection bodies.