Affine isoperimetric inequalities in the functional Orlicz-Brunn-Minkowski theory (1506.02974v2)

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 Santal\'o type inequalities.