A GENERAL $L_p$-VERSION OF PETTY'S AFFINE PROJECTION INEQUALITY

Abstract

About a decade ago Lutwak, Yang, and Zhang introduced the notion of $L_p$-projection body. More recently, Wang and Leng established an $L_p$-version of Petty's affine projection inequality. At the same time Ludwig discovered a family of general $L_p$-projection bodies and Haberl and Schuster established Petty's projection inequality for general $L_p$-projection bodies. In this paper we establish a general $L_p$-version of Petty's affine projection inequality for general $L_p$-projection bodies. Moreover, we obtain an analogous inequality for $L_p$-geominimal surface area.