Affine isoperimetric inequalities in the functional Orlicz-Brunn-Minkowski theory

Abstract

In this paper, we develop a basic theory of Orlicz affine and geominimal surface areas for convex and $s$-concave functions. We prove some basic properties for these newly introduced functional affine invariants and establish related functional affine isoperimetric inequalities as well as functional Santaló type inequalities.

The paper has a new title and has been revised completely