本项目基于申请人及其合作者在 2016年建立的一系列关于迷向测度的 Loomis-Whitney 型不等式。其目标是综合运用 M-加、质量迁移、积分变换等现代分析工具，来建立凸几何中的 Loomis-Whitney 型不等式。具体来说，我们将研究：关于对偶体积的 Meyer 不等式；关于内蕴体积的 Lp Loomis-Whitney 不等式的研究；关于 Lp-zonoid 的 Campi -Gronchi 不等式和 Campi-Gardner-Gronchi 不等式。

The project are based on the Loomis-Whitney type inequalities for isotropic measures established by the applicant and his collaborator in 2016. The purpose of the project is to establish Loomis-Whitney type inequalities in convex geometry analysis, by using the modern tools of M-addition, mass transportation, integral transformation etc. More specifically, we will focus on the following problems: the Meyer inequality for dual volumes; the Lp Loomis-Whitney inequality for intrinsic volumes; the Campi –Gronchi inequality and the Campi-Gardner-Gronchi inequality for Lp-zonoids.