Extending Bilipschitz Mappings between Separated Nets
arXiv:2507.22007 · doi:10.54330/afm.181562
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.
Accepted for publication in Annales Fennici Mathematici. Minor revision following the referee's report