IUMJ

Title: The mixed $L_p$ geominimal surface areas for multiple convex bodies

Authors: Deping Ye, Baocheng Zhu and Jiazu Zhou

Issue: Volume 64 (2015), Issue 5, 1513-1552

Abstract:

In this paper, we introduce several mixed $L_p$ geominimal surface areas for multiple convex bodies for all $-n\neq p\in\mathbb{R}$. Our definitions are motivated by an equivalent formula for the mixed $p$-affine surface area. Properties, such as the affine invariance, for these mixed $L_p$ geominimal surface areas are proved. Related Alexander-Fenchel type inequality, Santal\'o style inequalities, affine isoperimetric inequalities, and cyclic inequalities are established. Moreover, we also study properties and inequalities for the $i$-th mixed $L_p$ geominimal surface areas for two convex bodies.