--- _id: '10856' abstract: - lang: eng text: "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 \x1Cnd the optimal upper bound on the volume of a planar section of the cube [−1, 1]n , n ≥ 2." acknowledgement: "The authors acknowledge the support of the grant of the Russian Government N 075-15-\r\n2019-1926. 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." article_processing_charge: No article_type: original author: - first_name: Grigory full_name: Ivanov, Grigory id: 87744F66-5C6F-11EA-AFE0-D16B3DDC885E last_name: Ivanov - first_name: Igor full_name: Tsiutsiurupa, Igor last_name: Tsiutsiurupa citation: ama: 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 apa: 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 chicago: 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. ieee: 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. ista: Ivanov G, Tsiutsiurupa I. 2021. On the volume of sections of the cube. Analysis and Geometry in Metric Spaces. 9(1), 1–18. mla: 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. short: G. Ivanov, I. Tsiutsiurupa, Analysis and Geometry in Metric Spaces 9 (2021) 1–18. date_created: 2022-03-18T09:25:14Z date_published: 2021-01-29T00:00:00Z date_updated: 2023-08-17T07:07:58Z day: '29' ddc: - '510' department: - _id: UlWa doi: 10.1515/agms-2020-0103 external_id: arxiv: - '2004.02674' isi: - '000734286800001' file: - access_level: open_access checksum: 7e615ac8489f5eae580b6517debfdc53 content_type: application/pdf creator: dernst date_created: 2022-03-18T09:31:59Z date_updated: 2022-03-18T09:31:59Z file_id: '10857' file_name: 2021_AnalysisMetricSpaces_Ivanov.pdf file_size: 789801 relation: main_file success: 1 file_date_updated: 2022-03-18T09:31:59Z has_accepted_license: '1' intvolume: ' 9' isi: 1 issue: '1' keyword: - Applied Mathematics - Geometry and Topology - Analysis language: - iso: eng month: '01' oa: 1 oa_version: Published Version page: 1-18 publication: Analysis and Geometry in Metric Spaces publication_identifier: issn: - 2299-3274 publication_status: published publisher: De Gruyter quality_controlled: '1' scopus_import: '1' status: public title: On the volume of sections of the cube tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 9 year: '2021' ...