[{"OA_type":"hybrid","year":"2026","date_published":"2026-04-17T00:00:00Z","intvolume":"        51","author":[{"first_name":"Michael","full_name":"Dymond, Michael","last_name":"Dymond"},{"id":"21AE5134-9EAC-11EA-BEA2-D7BD3DDC885E","full_name":"Kaluza, Vojtech","last_name":"Kaluza","first_name":"Vojtech","orcid":"0000-0002-2512-8698"}],"citation":{"chicago":"Dymond, Michael, and Vojtech Kaluza. “Extending Bilipschitz Mappings between Separated Nets.” <i>Annales Fennici Mathematici</i>. Finnish Mathematical Society, 2026. <a href=\"https://doi.org/10.54330/afm.181562\">https://doi.org/10.54330/afm.181562</a>.","ista":"Dymond M, Kaluza V. 2026. Extending bilipschitz mappings between separated nets. Annales Fennici Mathematici. 51(1), 237–260.","short":"M. Dymond, V. Kaluza, Annales Fennici Mathematici 51 (2026) 237–260.","mla":"Dymond, Michael, and Vojtech Kaluza. “Extending Bilipschitz Mappings between Separated Nets.” <i>Annales Fennici Mathematici</i>, vol. 51, no. 1, Finnish Mathematical Society, 2026, pp. 237–60, doi:<a href=\"https://doi.org/10.54330/afm.181562\">10.54330/afm.181562</a>.","apa":"Dymond, M., &#38; Kaluza, V. (2026). Extending bilipschitz mappings between separated nets. <i>Annales Fennici Mathematici</i>. Finnish Mathematical Society. <a href=\"https://doi.org/10.54330/afm.181562\">https://doi.org/10.54330/afm.181562</a>","ieee":"M. Dymond and V. Kaluza, “Extending bilipschitz mappings between separated nets,” <i>Annales Fennici Mathematici</i>, vol. 51, no. 1. Finnish Mathematical Society, pp. 237–260, 2026.","ama":"Dymond M, Kaluza V. Extending bilipschitz mappings between separated nets. <i>Annales Fennici Mathematici</i>. 2026;51(1):237-260. doi:<a href=\"https://doi.org/10.54330/afm.181562\">10.54330/afm.181562</a>"},"language":[{"iso":"eng"}],"status":"public","has_accepted_license":"1","publisher":"Finnish Mathematical Society","article_processing_charge":"Yes (in subscription journal)","ddc":["510"],"corr_author":"1","doi":"10.54330/afm.181562","oa_version":"Published Version","abstract":[{"lang":"eng","text":"We provide a new characterisation of the decades old open problem of extending bilipschitz mappings given on a Euclidean separated net. In particular, this allows for the complete positive solution of the open problem in dimension two. Along the way, we develop a set of tools for bilipschitz extensions of mappings between subsets of Euclidean spaces."}],"file":[{"date_updated":"2026-04-28T12:03:13Z","file_size":342082,"file_id":"21772","creator":"dernst","success":1,"content_type":"application/pdf","checksum":"442023926a3803d5d6ca8db8dbc4af1c","date_created":"2026-04-28T12:03:13Z","file_name":"2026_AnnalesFenniciMath_Dymond.pdf","access_level":"open_access","relation":"main_file"}],"issue":"1","publication_status":"published","department":[{"_id":"UlWa"}],"article_type":"original","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","day":"17","date_created":"2026-04-26T22:01:47Z","project":[{"name":"Spectra and topology of graphs and of simplicial complexes","_id":"fc35eaa2-9c52-11eb-aca3-88501ab155e9","grant_number":"M03100"}],"date_updated":"2026-04-28T12:06:00Z","arxiv":1,"type":"journal_article","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by-nc/4.0/legalcode","name":"Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0)","image":"/images/cc_by_nc.png","short":"CC BY-NC (4.0)"},"keyword":["Lipschitz","bilipschitz","extension","separated net."],"title":"Extending bilipschitz mappings between separated nets","file_date_updated":"2026-04-28T12:03:13Z","publication":"Annales Fennici Mathematici","_id":"21766","month":"04","scopus_import":"1","quality_controlled":"1","external_id":{"arxiv":["2507.22007"]},"acknowledgement":"The present work developed from a research visit of M.D. to V.K. at IST Austria, funded by\r\na London Mathematical Society Research in Pairs grant. This work was done while V.K. was fully funded by the Austria Science Fund (FWF) [M 3100-N].","publication_identifier":{"eissn":["2737-114X"],"issn":["2737-0690"]},"OA_place":"publisher","page":"237-260","oa":1,"volume":51},{"date_updated":"2026-05-07T08:29:18Z","project":[{"grant_number":"M03100","_id":"fc35eaa2-9c52-11eb-aca3-88501ab155e9","name":"Spectra and topology of graphs and of simplicial complexes"}],"tmp":{"short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"arxiv":1,"type":"journal_article","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_type":"original","department":[{"_id":"UlWa"}],"issue":"4","publication_status":"published","date_created":"2026-05-03T22:01:37Z","day":"01","acknowledgement":"The authors wish to thank Professor Leonid Kovalev for a valuable observation on the first versionof this work, which led to improved estimates and cleaner proofs in Section 6. The present workdeveloped from a research visit of Michael Dymond to Vojtěch Kaluža at IST Austria, funded by aLondon Mathematical Society Research in Pairs grant. This work was done whilst Vojtěch Kalužawas fully funded by the Austria Science Fund (FWF) [M 3100-N].","publication_identifier":{"issn":["0024-6107"],"eissn":["1469-7750"]},"external_id":{"arxiv":["2410.22294"]},"article_number":"e70540","quality_controlled":"1","volume":113,"oa":1,"OA_place":"publisher","_id":"21778","file_date_updated":"2026-05-07T08:27:43Z","publication":"Journal of the London Mathematical Society","title":"Planar bilipschitz extension from separated nets","scopus_import":"1","month":"04","citation":{"mla":"Dymond, Michael, and Vojtech Kaluza. “Planar Bilipschitz Extension from Separated Nets.” <i>Journal of the London Mathematical Society</i>, vol. 113, no. 4, e70540, Wiley, 2026, doi:<a href=\"https://doi.org/10.1112/jlms.70540\">10.1112/jlms.70540</a>.","apa":"Dymond, M., &#38; Kaluza, V. (2026). Planar bilipschitz extension from separated nets. <i>Journal of the London Mathematical Society</i>. Wiley. <a href=\"https://doi.org/10.1112/jlms.70540\">https://doi.org/10.1112/jlms.70540</a>","ieee":"M. Dymond and V. Kaluza, “Planar bilipschitz extension from separated nets,” <i>Journal of the London Mathematical Society</i>, vol. 113, no. 4. Wiley, 2026.","ama":"Dymond M, Kaluza V. Planar bilipschitz extension from separated nets. <i>Journal of the London Mathematical Society</i>. 2026;113(4). doi:<a href=\"https://doi.org/10.1112/jlms.70540\">10.1112/jlms.70540</a>","chicago":"Dymond, Michael, and Vojtech Kaluza. “Planar Bilipschitz Extension from Separated Nets.” <i>Journal of the London Mathematical Society</i>. Wiley, 2026. <a href=\"https://doi.org/10.1112/jlms.70540\">https://doi.org/10.1112/jlms.70540</a>.","short":"M. Dymond, V. Kaluza, Journal of the London Mathematical Society 113 (2026).","ista":"Dymond M, Kaluza V. 2026. Planar bilipschitz extension from separated nets. Journal of the London Mathematical Society. 113(4), e70540."},"author":[{"last_name":"Dymond","full_name":"Dymond, Michael","first_name":"Michael"},{"full_name":"Kaluza, Vojtech","last_name":"Kaluza","id":"21AE5134-9EAC-11EA-BEA2-D7BD3DDC885E","orcid":"0000-0002-2512-8698","first_name":"Vojtech"}],"intvolume":"       113","status":"public","has_accepted_license":"1","language":[{"iso":"eng"}],"year":"2026","date_published":"2026-04-01T00:00:00Z","OA_type":"hybrid","oa_version":"Published Version","doi":"10.1112/jlms.70540","ddc":["510"],"file":[{"file_name":"2026_JourLondonMathSoc_Dymond.pdf","date_created":"2026-05-07T08:27:43Z","access_level":"open_access","relation":"main_file","checksum":"6dbfc7134f732d17c5c8467843a73e90","success":1,"content_type":"application/pdf","creator":"dernst","file_id":"21836","file_size":617569,"date_updated":"2026-05-07T08:27:43Z"}],"abstract":[{"text":"We prove that every 𝐿-bilipschitz mapping ℤ 2 → ℝ2 canbe extended to a 𝐶(𝐿)-bilipschitz mapping ℝ2 → ℝ2,and we provide a polynomial upper bound for 𝐶(𝐿).Moreover, we extend the result to every separated netin ℝ2 instead of ℤ 2, with the upper bound gaininga polynomial dependence on the separation and netconstants associated to the given separated net. Thisanswers an Oberwolfach question of Navas from 2015and is also a positive solution of the two-dimensionalform of a decades old open (in all dimensions at leasttwo) problem due to Alestalo Trotsenko and Väisälä.","lang":"eng"}],"publisher":"Wiley","article_processing_charge":"Yes (in subscription journal)"}]