Dual Orlicz-Brunn-Minkowski theory: dual Orlicz $L_{\phi}$ affine and   geominimal surface areas
  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. 
Deping Ye
math.MG math.DG math.FA