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On the volume of non-central sections of a cube Rudelson, Mark


Let $Q_n$ be the $n$-dimensional cube of side length one centered at the origin, and let $F$ be an affine $(n-d)$-dimensional subspace having distance to the origin less than or equal to $1/2$. We show that the $(n-d)$-dimensional volume of the section $Q_n$ by $F$ 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 $F$. Joint work with Hermann Koenig.

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