Every hyperplane section of the unit cube at distance at most 1/2 from the origin has (n-1)-dimensional volume greater than 1/17, with a complex analogue for polydiscs.
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On the volume of non-central sections of a cube
Every hyperplane section of the unit cube at distance at most 1/2 from the origin has (n-1)-dimensional volume greater than 1/17, with a complex analogue for polydiscs.