Concavity properties of extensions of the parallel volume

Abstract

In this paper we establish concavity properties of two extensions of the classical notion of the outer parallel volume. On the one hand, we replace the Lebesgue measure by more general measures. On the other hand, we consider a functional version of the outer parallel sets.

- Corrected typos - References updated - 19 pages

References in corpus (2)

• Weighted Poincaré-type inequalities for Cauchy and other convex measures
• A direct proof of the functional Santalo inequality