TY - JOUR
AB - 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.
AU - Ivanov, Grigory
AU - Tsiutsiurupa, Igor
ID - 10856
IS - 1
JF - Analysis and Geometry in Metric Spaces
KW - Applied Mathematics
KW - Geometry and Topology
KW - Analysis
SN - 2299-3274
TI - On the volume of sections of the cube
VL - 9
ER -