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