{"type":"journal_article","abstract":[{"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.","lang":"eng"}],"_id":"18483","author":[{"orcid":"0000-0002-6051-2628","full_name":"Kaloshin, Vadim","first_name":"Vadim","id":"FE553552-CDE8-11E9-B324-C0EBE5697425","last_name":"Kaloshin"},{"id":"52DF3E68-AEFA-11EA-95A4-124A3DDC885E","first_name":"Edmond","orcid":"0000-0003-2640-4049","full_name":"Koudjinan, Edmond","last_name":"Koudjinan"},{"last_name":"Zhang","first_name":"Ke","full_name":"Zhang, Ke"}],"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","file_date_updated":"2025-01-13T09:14:24Z","ec_funded":1,"year":"2024","tmp":{"short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png"},"date_published":"2024-12-01T00:00:00Z","intvolume":"        34","title":"Birkhoff conjecture for nearly centrally symmetric domains","status":"public","date_updated":"2025-09-08T14:27:45Z","doi":"10.1007/s00039-024-00695-6","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).","oa":1,"date_created":"2024-10-27T23:01:45Z","department":[{"_id":"VaKa"}],"publication_status":"published","month":"12","article_processing_charge":"Yes (via OA deal)","volume":34,"article_type":"original","OA_type":"hybrid","file":[{"file_id":"18833","creator":"dernst","file_size":2260980,"checksum":"e7fcd9f78beb40408c7d858ac0625e27","access_level":"open_access","success":1,"date_updated":"2025-01-13T09:14:24Z","date_created":"2025-01-13T09:14:24Z","content_type":"application/pdf","relation":"main_file","file_name":"2024_GeometricFunctionalAnalysis_Kaloshin.pdf"}],"quality_controlled":"1","publication":"Geometric and Functional Analysis","oa_version":"Published Version","language":[{"iso":"eng"}],"publisher":"Springer Nature","isi":1,"publication_identifier":{"issn":["1016-443X"],"eissn":["1420-8970"]},"arxiv":1,"ddc":["510"],"page":"1973-2007","OA_place":"publisher","project":[{"call_identifier":"H2020","grant_number":"885707","_id":"9B8B92DE-BA93-11EA-9121-9846C619BF3A","name":"Spectral rigidity and integrability for billiards and geodesic flows"}],"corr_author":"1","day":"01","scopus_import":"1","has_accepted_license":"1","external_id":{"arxiv":["2306.12301"],"isi":["001329804200001"]},"citation":{"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>.","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.","short":"V. Kaloshin, E. Koudjinan, K. Zhang, Geometric and Functional Analysis 34 (2024) 1973–2007.","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>"}}