article published yes Michael Dymond author Vojtech Kaluza author 21AE5134-9EAC-11EA-BEA2-D7BD3DDC885E0000-0002-2512-8698 UlWa department Spectra and topology of graphs and of simplicial complexes project 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. https://research-explorer.ista.ac.at/download/21778/21836/2026_JourLondonMathSoc_Dymond.pdf application/pdfno Wiley2026 eng 0024-6107 1469-7750 2410.2229410.1112/jlms.70540 1134 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>. 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>. 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> Dymond M, Kaluza V. 2026. Planar bilipschitz extension from separated nets. Journal of the London Mathematical Society. 113(4), e70540. 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> M. Dymond, V. Kaluza, Journal of the London Mathematical Society 113 (2026). 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. 217782026-05-03T22:01:37Z2026-05-07T08:29:18Z