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• W2969375488 abstract "Let $Q_n$ be the cube of side length one centered at the origin in $mathbb{R}^n$, and let $F$ be an affine $(n-d)$-dimensional subspace of $mathbb{R}^n$ having distance to the origin less than or equal to $frac 1 2$, where $0<d<n$. We show that the $(n-d)$-dimensional volume of the section $Q_n cap F$ is bounded below by a value $c(d)$ depending only on the codimension $d$ but not on the ambient dimension $n$ or a particular subspace $F$. In the case of hyperplanes, $d=1$, we show that $c(1) = frac{1}{17}$ is a possible choice. We also consider a complex analogue of this problem for a hyperplane section of the polydisc." @default.
• W2969375488 created "2019-08-29" @default.
• W2969375488 creator A5057215536 @default.
• W2969375488 creator A5089669144 @default.
• W2969375488 date "2019-08-25" @default.
• W2969375488 modified "2023-09-27" @default.
• W2969375488 title "On the volume of non-central sections of a cube" @default.
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