On the volume of sections of the cube
Ivanov G, Tsiutsiurupa I. 2021. On the volume of sections of the cube. Analysis and Geometry in Metric Spaces. 9(1), 1–18.
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Author
Ivanov, GrigoryISTA;
Tsiutsiurupa, Igor
Department
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.
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Publishing Year
Date Published
2021-01-29
Journal Title
Analysis and Geometry in Metric Spaces
Publisher
De Gruyter
Acknowledgement
The authors acknowledge the support of the grant of the Russian Government N 075-15-
2019-1926. G.I.was supported also by the SwissNational Science Foundation grant 200021-179133. The authors are very grateful to the anonymous reviewer for valuable remarks.
Volume
9
Issue
1
Page
1-18
ISSN
IST-REx-ID
Cite this
Ivanov G, Tsiutsiurupa I. On the volume of sections of the cube. Analysis and Geometry in Metric Spaces. 2021;9(1):1-18. doi:10.1515/agms-2020-0103
Ivanov, G., & Tsiutsiurupa, I. (2021). On the volume of sections of the cube. Analysis and Geometry in Metric Spaces. De Gruyter. https://doi.org/10.1515/agms-2020-0103
Ivanov, Grigory, and Igor Tsiutsiurupa. “On the Volume of Sections of the Cube.” Analysis and Geometry in Metric Spaces. De Gruyter, 2021. https://doi.org/10.1515/agms-2020-0103.
G. Ivanov and I. Tsiutsiurupa, “On the volume of sections of the cube,” Analysis and Geometry in Metric Spaces, vol. 9, no. 1. De Gruyter, pp. 1–18, 2021.
Ivanov G, Tsiutsiurupa I. 2021. On the volume of sections of the cube. Analysis and Geometry in Metric Spaces. 9(1), 1–18.
Ivanov, Grigory, and Igor Tsiutsiurupa. “On the Volume of Sections of the Cube.” Analysis and Geometry in Metric Spaces, vol. 9, no. 1, De Gruyter, 2021, pp. 1–18, doi:10.1515/agms-2020-0103.
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