[{"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"type":"journal_article","date_published":"2021-01-29T00:00:00Z","publication_identifier":{"issn":["2299-3274"]},"oa":1,"file":[{"access_level":"open_access","success":1,"relation":"main_file","file_id":"10857","creator":"dernst","date_created":"2022-03-18T09:31:59Z","file_size":789801,"checksum":"7e615ac8489f5eae580b6517debfdc53","date_updated":"2022-03-18T09:31:59Z","content_type":"application/pdf","file_name":"2021_AnalysisMetricSpaces_Ivanov.pdf"}],"status":"public","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","has_accepted_license":"1","publication":"Analysis and Geometry in Metric Spaces","oa_version":"Published Version","month":"01","keyword":["Applied Mathematics","Geometry and Topology","Analysis"],"language":[{"iso":"eng"}],"year":"2021","citation":{"mla":"Ivanov, Grigory, and Igor Tsiutsiurupa. “On the Volume of Sections of the Cube.” <i>Analysis and Geometry in Metric Spaces</i>, vol. 9, no. 1, De Gruyter, 2021, pp. 1–18, doi:<a href=\"https://doi.org/10.1515/agms-2020-0103\">10.1515/agms-2020-0103</a>.","short":"G. Ivanov, I. Tsiutsiurupa, Analysis and Geometry in Metric Spaces 9 (2021) 1–18.","ista":"Ivanov G, Tsiutsiurupa I. 2021. On the volume of sections of the cube. Analysis and Geometry in Metric Spaces. 9(1), 1–18.","ama":"Ivanov G, Tsiutsiurupa I. On the volume of sections of the cube. <i>Analysis and Geometry in Metric Spaces</i>. 2021;9(1):1-18. doi:<a href=\"https://doi.org/10.1515/agms-2020-0103\">10.1515/agms-2020-0103</a>","apa":"Ivanov, G., &#38; Tsiutsiurupa, I. (2021). On the volume of sections of the cube. <i>Analysis and Geometry in Metric Spaces</i>. De Gruyter. <a href=\"https://doi.org/10.1515/agms-2020-0103\">https://doi.org/10.1515/agms-2020-0103</a>","chicago":"Ivanov, Grigory, and Igor Tsiutsiurupa. “On the Volume of Sections of the Cube.” <i>Analysis and Geometry in Metric Spaces</i>. De Gruyter, 2021. <a href=\"https://doi.org/10.1515/agms-2020-0103\">https://doi.org/10.1515/agms-2020-0103</a>.","ieee":"G. Ivanov and I. Tsiutsiurupa, “On the volume of sections of the cube,” <i>Analysis and Geometry in Metric Spaces</i>, vol. 9, no. 1. De Gruyter, pp. 1–18, 2021."},"date_updated":"2023-08-17T07:07:58Z","external_id":{"arxiv":["2004.02674"],"isi":["000734286800001"]},"isi":1,"day":"29","doi":"10.1515/agms-2020-0103","arxiv":1,"abstract":[{"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 \u001cnd the optimal upper bound on the volume of a planar section of the cube [−1, 1]n , n ≥ 2.","lang":"eng"}],"volume":9,"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.","ddc":["510"],"scopus_import":"1","_id":"10856","issue":"1","author":[{"full_name":"Ivanov, Grigory","first_name":"Grigory","last_name":"Ivanov","id":"87744F66-5C6F-11EA-AFE0-D16B3DDC885E"},{"last_name":"Tsiutsiurupa","first_name":"Igor","full_name":"Tsiutsiurupa, Igor"}],"department":[{"_id":"UlWa"}],"article_processing_charge":"No","date_created":"2022-03-18T09:25:14Z","publication_status":"published","intvolume":"         9","title":"On the volume of sections of the cube","quality_controlled":"1","page":"1-18","file_date_updated":"2022-03-18T09:31:59Z","publisher":"De Gruyter","article_type":"original"}]