Towards bilipschitz extension from euclidean separated nets of general dimension

Michael Dymond; Vojtěch Kaluža

doi:10.48550/arXiv.2507.22007

Towards bilipschitz extension from euclidean separated nets of general dimension

Michael Dymond
, Vojtěch Kaluža

Mathematics

Research output: Working paper/Preprint › Preprint

Abstract

We provide a foundation for an approach to the open problem of bilipschitz extendability of mappings defined on a Euclidean separated net. In particular, this allows for the complete positive solution of the problem in dimension two. Along the way, we develop a set of tools for bilipschitz extensions of mappings between subsets of Euclidean spaces.

Original language	English
Publisher	arXiv
DOIs	https://doi.org/10.48550/arXiv.2507.22007
Publication status	Published - 29 Jul 2025

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abstract = "We provide a foundation for an approach to the open problem of bilipschitz extendability of mappings defined on a Euclidean separated net. In particular, this allows for the complete positive solution of the 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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Towards bilipschitz extension from euclidean separated nets of general dimension

Abstract

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