On the Volume of Sections of the Cube
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 t...
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De Gruyter
2021
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oai:doaj.org-article:8b4c095f33f9465a8d086a653517305c2021-12-05T14:10:38ZOn the Volume of Sections of the Cube2299-327410.1515/agms-2020-0103https://doaj.org/article/8b4c095f33f9465a8d086a653517305c2021-01-01T00:00:00Zhttps://doi.org/10.1515/agms-2020-0103https://doaj.org/toc/2299-3274We 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.Ivanov GrigoryTsiutsiurupa IgorDe Gruyterarticletight framesection of cubevolumeball’s inequality52a3849q2052a4015a45AnalysisQA299.6-433ENAnalysis and Geometry in Metric Spaces, Vol 9, Iss 1, Pp 1-18 (2021) |
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DOAJ |
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DOAJ |
| language |
EN |
| topic |
tight frame section of cube volume ball’s inequality 52a38 49q20 52a40 15a45 Analysis QA299.6-433 |
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tight frame section of cube volume ball’s inequality 52a38 49q20 52a40 15a45 Analysis QA299.6-433 Ivanov Grigory Tsiutsiurupa Igor On the Volume of Sections of the Cube |
| description |
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. |
| format |
article |
| author |
Ivanov Grigory Tsiutsiurupa Igor |
| author_facet |
Ivanov Grigory Tsiutsiurupa Igor |
| author_sort |
Ivanov Grigory |
| title |
On the Volume of Sections of the Cube |
| title_short |
On the Volume of Sections of the Cube |
| title_full |
On the Volume of Sections of the Cube |
| title_fullStr |
On the Volume of Sections of the Cube |
| title_full_unstemmed |
On the Volume of Sections of the Cube |
| title_sort |
on the volume of sections of the cube |
| publisher |
De Gruyter |
| publishDate |
2021 |
| url |
https://doaj.org/article/8b4c095f33f9465a8d086a653517305c |
| work_keys_str_mv |
AT ivanovgrigory onthevolumeofsectionsofthecube AT tsiutsiurupaigor onthevolumeofsectionsofthecube |
| _version_ |
1718371850913841152 |