Grünbaum's inequality for projections

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• 作者：M. Stephen ; ^{mastephe@ualberta.ca} ; N. Zhang ^{nzhang2@ualberta.ca}
• 关键词：Centroid ; Convex bodies ; Grü ; nbaum's inequality ; Projections
• 刊名：Journal of Functional Analysis
• 出版年：2017
• 出版时间：15 March 2017
• 年：2017
• 卷：272
• 期：6
• 页码：2628-2640
• 全文大小：299 K
• 卷排序：272

文摘

Let K   be a convex body in RnRn whose centroid is at the origin, let E∈G(n,k)E∈G(n,k) be a subspace, and let ξ∈Sn−1ξ∈Sn−1. We find the best constant c=(kn+1)k so that |(K|E)∩ξ+|k≥c|K|E|k, and completely determine the minimizer. Here, |⋅|k|⋅|k is k  -dimensional volume, K|EK|E is the projection of K onto E  , and ξ+={x∈Rn:〈x,ξ〉≥0}. Our result generalizes both Grünbaum's inequality, and an old inequality of Minkowski and Radon.