Extending bilipschitz mappings between separated nets

Michael Dymond; Vojtěch Kaluža

Extending bilipschitz mappings between separated nets

Michael Dymond
, Vojtěch Kaluža

Mathematics

Research output: Working paper/Preprint › Preprint

Abstract

We prove that every L-bilipschitz mapping ℤ²→ℝ² can be extended to a C(L)-bilipschitz mapping ℝ²→ℝ² and provide an upper bound for C(L). Moreover, we extend the result to every separated net in ℝ² instead of ℤ². Along the way, we develop a set of tools for bilipschitz extensions of mappings between subsets of Euclidean spaces.

Original language	English
Publisher	arXiv
Publication status	Published - 29 Oct 2024

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https://arxiv.org/abs/2410.22294Licence: Creative Commons: Attribution (CC BY)

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title = "Extending bilipschitz mappings between separated nets",

abstract = "We prove that every L-bilipschitz mapping ℤ2→ℝ2 can be extended to a C(L)-bilipschitz mapping ℝ2→ℝ2 and provide an upper bound for C(L). Moreover, we extend the result to every separated net in ℝ2 instead of ℤ2. Along the way, we develop a set of tools for bilipschitz extensions of mappings between subsets of Euclidean spaces.",

author = "Michael Dymond and Vojt{\v e}ch Kalu{\v z}a",

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AU - Kaluža, Vojtěch

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N2 - We prove that every L-bilipschitz mapping ℤ2→ℝ2 can be extended to a C(L)-bilipschitz mapping ℝ2→ℝ2 and provide an upper bound for C(L). Moreover, we extend the result to every separated net in ℝ2 instead of ℤ2. Along the way, we develop a set of tools for bilipschitz extensions of mappings between subsets of Euclidean spaces.

AB - We prove that every L-bilipschitz mapping ℤ2→ℝ2 can be extended to a C(L)-bilipschitz mapping ℝ2→ℝ2 and provide an upper bound for C(L). Moreover, we extend the result to every separated net in ℝ2 instead of ℤ2. Along the way, we develop a set of tools for bilipschitz extensions of mappings between subsets of Euclidean spaces.

M3 - Preprint

BT - Extending bilipschitz mappings between separated nets

PB - arXiv

ER -

Extending bilipschitz mappings between separated nets

Abstract

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