# MathSciDoc: An Archive for Mathematician ∫

#### Convex and Discrete Geometry mathscidoc:1703.40023

Bull. London Math. Soc., 48, 676–690, 2016
We establish a dual version of the Loomis-Whitney inequality for isotropic measures with complete equality conditions, where the sharp lower bound is given in terms of the volumes of hyperplane sections. For the special case of cross measures, we can drop the condition that the underlying body has centroid at the origin, yielding an independent proof of a result of Meyer's.
Loomis-Whitney inequality, hyperplane sections, generalized $\ell_1^n$-ball.
@inproceedings{ai-jun2016the,
title={The dual Loomis-Whitney inequality},
author={Ai-Jun Li, and Qingzhong Huang},
url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170304091710435701609},
booktitle={Bull. London Math. Soc.},
volume={48},
pages={676–690},
year={2016},
}

Ai-Jun Li, and Qingzhong Huang. The dual Loomis-Whitney inequality. 2016. Vol. 48. In Bull. London Math. Soc.. pp.676–690. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170304091710435701609.