@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},
}