$L_p$-Centroid Bodies and Its Characterizations (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 isobtained. In addition, using the definitions of $L_p$-pole curvature image and $L_p$-affinesurface area, a new proof of Busemann-Petty problem for $L_p$-centroid bodies is given.