Extending Bilipschitz Mappings between Separated Nets
Michael Dymond, Vojt\v{e}ch Kalu\v{z}a
TL;DR
This paper advances the understanding of extending bilipschitz mappings on separated nets in Euclidean spaces, providing a complete solution in two dimensions and developing new tools for such extensions.
Contribution
It offers a new characterization of the longstanding open problem and introduces tools for bilipschitz extensions between Euclidean subsets.
Findings
Complete positive solution for dimension two
New tools for bilipschitz extension problems
Enhanced understanding of separated nets in Euclidean spaces
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.
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Taxonomy
TopicsOptimization and Variational Analysis · Advanced Banach Space Theory · Fixed Point Theorems Analysis