Security Steiner’s Inequality on Layering Functions

Abstract

The classical definition of Steiner symmetrizations of functions are defined according to the Steiner symmetrizations of function level sets and the layered representation of functions. In this paper, the definition is not only transformed into Steiner symmetrizations of one-dimensional parabolic functions, but also depends on the Steiner symmetrizations of the level sets of log-concave functions. To this end we prove Steiner’s inequality on layering functions in the space of log-concave functions.