(untitled) (Communications in Mathematical Research, 2021)
In this paper, we study the characteristic properties for L_p-centroid bodies, and an improved version of Busemann-Petty problem for L_p-centroid bodies is obtained. In addition, using the definitions of L_p-pole curvature image and L_p-affine surface area, a new proof of Busemann-Petty problem for L_p-centroid bodies is given.