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 Santal\'o type inequalities.
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