Extending bilipschitz mappings between separated nets
Abstract
Abstract We prove that every ‐bilipschitz mapping can be extended to a ‐bilipschitz mapping , and we provide a polynomial upper bound for . Moreover, we extend the result to every separated net in instead of , with the upper bound gaining a polynomial dependence on the separation and net constants associated to the given separated net. This answers an Oberwolfach question of Navas from 2015 and is also a positive solution of the two‐dimensional form of a decades old open (in all dimensions at least two) problem due to Alestalo Trotsenko and Väisälä.
Fields of Study & Subjects
Data Management and Algorithms
Rough Sets and Fuzzy Logic
Advanced Database Systems and Queries
Publication details
- Journal / source
- Journal of the London Mathematical Society
- Volume
- 113
- Issue
- 1
- Pages
- 237–260
- Publication date
- 1 April 2026
- Language
- EN