Towards bilipschitz extension from euclidean separated nets of general dimension

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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