[{"title":"On the volume of sections of the cube","external_id":{"arxiv":["2004.02674"],"isi":["000734286800001"]},"doi":"10.1515/agms-2020-0103","year":"2021","ddc":["510"],"isi":1,"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)"},"author":[{"id":"87744F66-5C6F-11EA-AFE0-D16B3DDC885E","last_name":"Ivanov","full_name":"Ivanov, Grigory","first_name":"Grigory"},{"first_name":"Igor","full_name":"Tsiutsiurupa, Igor","last_name":"Tsiutsiurupa"}],"keyword":["Applied Mathematics","Geometry and Topology","Analysis"],"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."}],"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>","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.","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>","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>.","ista":"Ivanov G, Tsiutsiurupa I. 2021. On the volume of sections of the cube. Analysis and Geometry in Metric Spaces. 9(1), 1–18.","short":"G. Ivanov, I. Tsiutsiurupa, Analysis and Geometry in Metric Spaces 9 (2021) 1–18."},"publication_status":"published","quality_controlled":"1","oa_version":"Published Version","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","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.","publication_identifier":{"issn":["2299-3274"]},"_id":"10856","article_processing_charge":"No","volume":9,"date_updated":"2023-08-17T07:07:58Z","oa":1,"arxiv":1,"language":[{"iso":"eng"}],"scopus_import":"1","publisher":"De Gruyter","date_published":"2021-01-29T00:00:00Z","article_type":"original","month":"01","file":[{"success":1,"file_id":"10857","creator":"dernst","content_type":"application/pdf","relation":"main_file","date_created":"2022-03-18T09:31:59Z","checksum":"7e615ac8489f5eae580b6517debfdc53","file_name":"2021_AnalysisMetricSpaces_Ivanov.pdf","file_size":789801,"date_updated":"2022-03-18T09:31:59Z","access_level":"open_access"}],"date_created":"2022-03-18T09:25:14Z","department":[{"_id":"UlWa"}],"has_accepted_license":"1","status":"public","intvolume":"         9","type":"journal_article","day":"29","file_date_updated":"2022-03-18T09:31:59Z","page":"1-18","publication":"Analysis and Geometry in Metric Spaces","issue":"1"}]