---
_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
arxiv: 1
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. <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.
  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>.
  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'
...