The mixed $L_p$ geominimal surface areas for multiple convex bodies
Metric Geometry
2016-06-07 v1 Differential Geometry
Abstract
In this paper, we introduce several mixed geominimal surface areas for multiple convex bodies for all . Our definitions are motivated from an equivalent formula for the mixed -affine surface area. Some properties, such as the affine invariance, for these mixed geominimal surface areas are proved. Related inequalities, such as, Alexander-Fenchel type inequality, Santal\'{o} style inequality, affine isoperimetric inequalities, and cyclic inequalities are established. Moreover, we also study some properties and inequalities for the -th mixed geominimal surface areas for two convex bodies.
Keywords
Cite
@article{arxiv.1311.5180,
title = {The mixed $L_p$ geominimal surface areas for multiple convex bodies},
author = {Deping Ye and Baocheng Zhu and Jiazu Zhou},
journal= {arXiv preprint arXiv:1311.5180},
year = {2016}
}