Extending Bilipschitz Mappings between Separated Nets
Metric Geometry
2026-03-20 v3 Functional Analysis
Abstract
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.
Cite
@article{arxiv.2507.22007,
title = {Extending Bilipschitz Mappings between Separated Nets},
author = {Michael Dymond and Vojtěch Kaluža},
journal= {arXiv preprint arXiv:2507.22007},
year = {2026}
}
Comments
Accepted for publication in Annales Fennici Mathematici. Minor revision following the referee's report