[{"OA_place":"publisher","volume":51,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"last_name":"Dymond","first_name":"Michael","full_name":"Dymond, Michael"},{"last_name":"Kaluza","first_name":"Vojtech","orcid":"0000-0002-2512-8698","id":"21AE5134-9EAC-11EA-BEA2-D7BD3DDC885E","full_name":"Kaluza, Vojtech"}],"title":"Extending bilipschitz mappings between separated nets","keyword":["Lipschitz","bilipschitz","extension","separated net."],"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."}],"publication_status":"published","external_id":{"arxiv":["2507.22007"]},"page":"237-260","license":"https://creativecommons.org/licenses/by-nc/4.0/","article_processing_charge":"Yes (in subscription journal)","publication":"Annales Fennici Mathematici","issue":"1","publication_identifier":{"eissn":["2737-114X"],"issn":["2737-0690"]},"doi":"10.54330/afm.181562","year":"2026","date_created":"2026-04-26T22:01:47Z","ddc":["510"],"has_accepted_license":"1","file":[{"content_type":"application/pdf","file_name":"2026_AnnalesFenniciMath_Dymond.pdf","date_created":"2026-04-28T12:03:13Z","creator":"dernst","success":1,"file_id":"21772","date_updated":"2026-04-28T12:03:13Z","file_size":342082,"relation":"main_file","checksum":"442023926a3803d5d6ca8db8dbc4af1c","access_level":"open_access"}],"quality_controlled":"1","corr_author":"1","_id":"21766","scopus_import":"1","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].","type":"journal_article","article_type":"original","intvolume":"        51","oa_version":"Published Version","department":[{"_id":"UlWa"}],"arxiv":1,"publisher":"Finnish Mathematical Society","date_updated":"2026-04-28T12:06:00Z","month":"04","language":[{"iso":"eng"}],"date_published":"2026-04-17T00:00:00Z","oa":1,"file_date_updated":"2026-04-28T12:03:13Z","day":"17","status":"public","OA_type":"hybrid","tmp":{"short":"CC BY-NC (4.0)","name":"Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0)","image":"/images/cc_by_nc.png","legal_code_url":"https://creativecommons.org/licenses/by-nc/4.0/legalcode"},"project":[{"_id":"fc35eaa2-9c52-11eb-aca3-88501ab155e9","grant_number":"M03100","name":"Spectra and topology of graphs and of simplicial complexes"}],"citation":{"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>","ista":"Dymond M, Kaluza V. 2026. Extending bilipschitz mappings between separated nets. Annales Fennici Mathematici. 51(1), 237–260.","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.","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>.","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>.","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>"}}]