Based on reverse isoperimetric inequalities on Grassmann manifolds, a Grassmanian Loomis–Whitney inequality and its dual are established, which provides a lower bound for the volume of an origin‐symmetric convex body in terms of its lower dimensional sections.

中文翻译：

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Grassmannian Loomis-Whitney不等式及其对偶

基于格拉斯曼流形上的反向等距不等式，建立了格拉斯曼鲁米斯-惠特尼不等式及其对偶式，这为低对称截面的原点对称凸体的体积提供了下限。