Chord power integrals and radial mean bodies

In this paper, we obtain a formula relating the chord power integrals of a convex body K and the dual quermassintegrals of its radial pth mean body RpK. With this, a relation among the chord power integrals of a convex body K under dilation transformations is found. As an interesting application, some geometric inequalities between the dual quermassintegrals of RpK and the volume of K, which are equivalent to the isoperimetric-type inequalities of chord power integrals, are also established. © 2007 Elsevier Inc. All rights reserved