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Dual Orlicz-Brunn-Minkowski theory: dual Orlicz $L_φ$ affine and geominimal surface areas (1405.0746v2)
Published 4 May 2014 in math.MG, math.DG, and math.FA
Abstract: This paper aims to develop basic theory for the dual Orlicz $L_{\phi}$ affine and geominimal surface areas for star bodies, which belong to the recent dual Orlicz-Brunn-Minkowski theory for star bodies. Basic properties for these new affine invariants will be provided. Moreover, related Orlicz affine isoperimetric inequality, cyclic inequality, Santal\'{o} style inequality and Alexander-Fenchel type inequality are established.