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

Published 9 Jun 2015 in math.MG and math.FA | (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.

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