[{"creator":{"login":"dernst","id":"2DF688A6-F248-11E8-B48F-1D18A9856A87"},"file_date_updated":"2022-03-18T09:31:59Z","department":[{"_id":"UlWa","tree":[{"_id":"ResearchGroups"},{"_id":"IST"}]}],"publication_status":"published","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.","volume":9,"dini_type":"doc-type:article","date_created":"2022-03-18T09:25:14Z","date_updated":"2023-08-17T07:07:58Z","author":[{"first_name":"Grigory","last_name":"Ivanov","id":"87744F66-5C6F-11EA-AFE0-D16B3DDC885E"},{"first_name":"Igor","last_name":"Tsiutsiurupa"}],"publication_identifier":{"issn":[]},"month":"01","isi":1,"quality_controlled":"1","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"external_id":{"arxiv":[],"isi":[]},"oa":1,"language":[{}],"type":"journal_article","issue":"1","abstract":[{"lang":"eng"}],"intvolume":" 9","ddc":[],"status":"public","_id":"10856","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","file":[{"creator":"dernst","file_size":789801,"content_type":"application/pdf","file_name":"2021_AnalysisMetricSpaces_Ivanov.pdf","access_level":"open_access","date_updated":"2022-03-18T09:31:59Z","date_created":"2022-03-18T09:31:59Z","success":1,"checksum":"7e615ac8489f5eae580b6517debfdc53","file_id":"10857","relation":"main_file"}],"oa_version":"Published Version","keyword":[],"dc":{"relation":["info:eu-repo/semantics/altIdentifier/doi/10.1515/agms-2020-0103","info:eu-repo/semantics/altIdentifier/issn/2299-3274","info:eu-repo/semantics/altIdentifier/wos/000734286800001","info:eu-repo/semantics/altIdentifier/arxiv/2004.02674"],"subject":["Applied Mathematics","Geometry and Topology","Analysis","ddc:510"],"publisher":["De Gruyter"],"title":["On the volume of sections of the cube"],"source":["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"],"rights":["info:eu-repo/semantics/openAccess"],"language":["eng"],"date":["2021"],"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 \u001cnd the optimal upper bound on the volume of a planar section of the cube [−1, 1]n , n ≥ 2."],"identifier":["https://research-explorer.ista.ac.at/record/10856","https://research-explorer.ista.ac.at/download/10856/10857"],"type":["info:eu-repo/semantics/article","doc-type:article","text","http://purl.org/coar/resource_type/c_6501"],"creator":["Ivanov, Grigory","Tsiutsiurupa, Igor"]},"scopus_import":"1","article_processing_charge":"No","uri_base":"https://research-explorer.ista.ac.at","has_accepted_license":"1","day":"29","page":"1-18","article_type":"original","citation":{"ista":"Ivanov G, Tsiutsiurupa I. 2021. On the volume of sections of the cube. Analysis and Geometry in Metric Spaces. 9(1), 1–18.","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.","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","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.","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."},"publication":"Analysis and Geometry in Metric Spaces","date_published":"2021-01-29T00:00:00Z"}]