---
OA_place: publisher
OA_type: hybrid
_id: '18483'
abstract:
- lang: eng
  text: In this paper we prove a perturbative version of a remarkable Bialy–Mironov
    (Ann. Math. 196(1):389–413, 2022) result. They prove non perturbative Birkhoff
    conjecture for centrally-symmetric convex domains, namely, a centrally-symmetric
    convex domain with integrable billiard is ellipse. We combine techniques from
    Bialy–Mironov (Ann. Math. 196(1):389–413, 2022) with a local result by Kaloshin–Sorrentino
    (Ann. Math. 188(1):315–380, 2018) and show that a domain close enough to a centrally
    symmetric one with integrable billiard is ellipse. To combine these results we
    derive a slight extension of Bialy–Mironov (Ann. Math. 196(1):389–413, 2022) by
    proving that a notion of rational integrability is equivalent to the C0-integrability
    condition used in their paper.
acknowledgement: We are grateful to the anonymous referee for their careful reading
  and valuable remarks and comments which helped to improve significantly the paper.
  Open access funding provided by Institute of Science and Technology (IST Austria).
  V.K. and C.E.K. gratefully acknowledge support from the European Research Council
  (ERC) through the Advanced Grant “SPERIG” (#885 707).
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Vadim
  full_name: Kaloshin, Vadim
  id: FE553552-CDE8-11E9-B324-C0EBE5697425
  last_name: Kaloshin
  orcid: 0000-0002-6051-2628
- first_name: Edmond
  full_name: Koudjinan, Edmond
  id: 52DF3E68-AEFA-11EA-95A4-124A3DDC885E
  last_name: Koudjinan
  orcid: 0000-0003-2640-4049
- first_name: Ke
  full_name: Zhang, Ke
  last_name: Zhang
citation:
  ama: Kaloshin V, Koudjinan E, Zhang K. Birkhoff conjecture for nearly centrally
    symmetric domains. <i>Geometric and Functional Analysis</i>. 2024;34:1973-2007.
    doi:<a href="https://doi.org/10.1007/s00039-024-00695-6">10.1007/s00039-024-00695-6</a>
  apa: Kaloshin, V., Koudjinan, E., &#38; Zhang, K. (2024). Birkhoff conjecture for
    nearly centrally symmetric domains. <i>Geometric and Functional Analysis</i>.
    Springer Nature. <a href="https://doi.org/10.1007/s00039-024-00695-6">https://doi.org/10.1007/s00039-024-00695-6</a>
  chicago: Kaloshin, Vadim, Edmond Koudjinan, and Ke Zhang. “Birkhoff Conjecture for
    Nearly Centrally Symmetric Domains.” <i>Geometric and Functional Analysis</i>.
    Springer Nature, 2024. <a href="https://doi.org/10.1007/s00039-024-00695-6">https://doi.org/10.1007/s00039-024-00695-6</a>.
  ieee: V. Kaloshin, E. Koudjinan, and K. Zhang, “Birkhoff conjecture for nearly centrally
    symmetric domains,” <i>Geometric and Functional Analysis</i>, vol. 34. Springer
    Nature, pp. 1973–2007, 2024.
  ista: Kaloshin V, Koudjinan E, Zhang K. 2024. Birkhoff conjecture for nearly centrally
    symmetric domains. Geometric and Functional Analysis. 34, 1973–2007.
  mla: Kaloshin, Vadim, et al. “Birkhoff Conjecture for Nearly Centrally Symmetric
    Domains.” <i>Geometric and Functional Analysis</i>, vol. 34, Springer Nature,
    2024, pp. 1973–2007, doi:<a href="https://doi.org/10.1007/s00039-024-00695-6">10.1007/s00039-024-00695-6</a>.
  short: V. Kaloshin, E. Koudjinan, K. Zhang, Geometric and Functional Analysis 34
    (2024) 1973–2007.
corr_author: '1'
date_created: 2024-10-27T23:01:45Z
date_published: 2024-12-01T00:00:00Z
date_updated: 2025-09-08T14:27:45Z
day: '01'
ddc:
- '510'
department:
- _id: VaKa
doi: 10.1007/s00039-024-00695-6
ec_funded: 1
external_id:
  arxiv:
  - '2306.12301'
  isi:
  - '001329804200001'
file:
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  creator: dernst
  date_created: 2025-01-13T09:14:24Z
  date_updated: 2025-01-13T09:14:24Z
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has_accepted_license: '1'
intvolume: '        34'
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language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
month: '12'
oa: 1
oa_version: Published Version
page: 1973-2007
project:
- _id: 9B8B92DE-BA93-11EA-9121-9846C619BF3A
  call_identifier: H2020
  grant_number: '885707'
  name: Spectral rigidity and integrability for billiards and geodesic flows
publication: Geometric and Functional Analysis
publication_identifier:
  eissn:
  - 1420-8970
  issn:
  - 1016-443X
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Birkhoff conjecture for nearly centrally symmetric domains
tmp:
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  name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
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type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 34
year: '2024'
...