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