Inequalities for inscribed simplex and applications.
We establish Brunn-Minkowski type inequalities for radial Blaschke-Minkowski homomorphisms, which in special cases yield some new results for intersection bodies. Moreover, we obtain two monotonicity inequalities for radial Blaschke-Minkowski homomorphisms.
We extend Kahane-Khinchin type inequalities to the case p > -2. As an application we verify the slicing problem for the unit balls of finite-dimensional spaces that embed in , p > -2.