On the volume of sections of the cube

2020/04/06 by Ivanov, Grigory, Tsiutsiurupa, Igor · 3 citations
#15A45 #49Q20 #52A38 #52A40 #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.2004.02674

Abstract

We study the properties of the maximal volume k-dimensional sections of the n-dimensional cube [-1,1]ⁿ. We obtain a first order necessary condition for a k-dimensional subspace to be a local maximizer of the volume of such sections, which we formulate in a geometric way. We estimate the length of the projection of a vector of the standard basis of ℝⁿ onto a k-dimensional subspace that maximizes the volume of the intersection. We find the optimal upper bound on the volume of a planar section of the cube [-1,1]ⁿ, n ≥ 2.

Cited by

• Central diagonal sections of Gaussian n-cubes
• Combinatorics of slices of cubes
• John Ellipsoids of Revolution

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