Planar bilipschitz extension from separated nets Dymond, Michael Kaluza, Vojtech ; https://orcid.org/0000-0002-2512-8698 ddc:510 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. Wiley 2026 info:eu-repo/semantics/article doc-type:article text http://purl.org/coar/resource_type/c_2df8fbb1 https://research-explorer.ista.ac.at/record/21778 https://research-explorer.ista.ac.at/download/21778/21836 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> eng info:eu-repo/semantics/altIdentifier/doi/10.1112/jlms.70540 info:eu-repo/semantics/altIdentifier/issn/0024-6107 info:eu-repo/semantics/altIdentifier/e-issn/1469-7750 info:eu-repo/semantics/altIdentifier/arxiv/2410.22294 info:eu-repo/semantics/openAccess