@article{10856,
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 nd the optimal upper bound on the volume of a planar section of the cube [−1, 1]n , n ≥ 2.},
author = {Ivanov, Grigory and Tsiutsiurupa, Igor},
issn = {2299-3274},
journal = {Analysis and Geometry in Metric Spaces},
keywords = {Applied Mathematics, Geometry and Topology, Analysis},
number = {1},
pages = {1--18},
publisher = {De Gruyter},
title = {{On the volume of sections of the cube}},
doi = {10.1515/agms-2020-0103},
volume = {9},
year = {2021},
}