Busemann-Petty Type Problem for the General $L_p$-Centroid Bodies

Abstract

Lutwak showed the Busemann-Petty type problem (also called the Shephard type problem) for the centroid bodies. Grinberg and Zhang gave an affirmation and a negative form of the Busemann-Petty type problem for the $L_p$-centroid bodies. In this paper, we obtain an affirmation form and two negative forms of the Busemann-Petty type problem for the general $L_p$-centroid bodies.