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arXiv · 1311.5180

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

Deping Ye·Baocheng Zhu·Jiazu Zhou
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Abstract

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

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Deping Ye, Baocheng Zhu, Jiazu Zhou. 2013-11-20. The mixed $L_p$ geominimal surface areas for multiple convex bodies. https://doi.org/10.1512/iumj.2015.64.5623

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