On the reverse Orlicz Busemann-Petty centroid inequality

In this paper, the Orlicz centroid body, defined by E. Lutwak, D. Yang and G. Zhang, and the extrema of some affine invariant functionals involving the volume of the Orlicz centroid body are investigated. The reverse form of the Orlicz Busemann-Petty centroid inequalities is obtained in the two-dimensional case.