Bi-Lipschitz embeddings of quasiconformal trees

David, Guy; Eriksson-Bique, Sylvester; Vellis, Vyron

doi:10.1090/proc/16252

Bi-Lipschitz embeddings of quasiconformal trees
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by Guy C. David, Sylvester Eriksson-Bique and Vyron Vellis;

Proc. Amer. Math. Soc. 151 (2023), 2031-2044

DOI: https://doi.org/10.1090/proc/16252

Published electronically: February 2, 2023

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Abstract:

A quasiconformal tree is a doubling metric tree in which the diameter of each arc is bounded above by a fixed multiple of the distance between its endpoints. In this paper we show that every quasiconformal tree bi-Lipschitz embeds in some Euclidean space, with the ambient dimension and the bi-Lipschitz constant depending only on the doubling and bounded turning constants of the tree. This answers Question 1.6 of David and Vellis [Illinois J. Math. 66 (2022), pp. 189–244].

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