TY - JOUR T1 - $L_p$-Centroid Bodies and Its Characterizations AU - Ma , Tongyi AU - Zhang , Deyan JO - Communications in Mathematical Research VL - 4 SP - 333 EP - 344 PY - 2021 DA - 2021/05 SN - 31 DO - http://doi.org/10.13447/j.1674-5647.2015.04.05 UR - https://global-sci.org/intro/article_detail/cmr/18914.html KW - convex body, star body, centroid body, $L_p$-centroid body, Busemann-Petty problem. AB -

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.