Bi-Lipschitz embeddings of quasiconformal trees
Metric Geometry
2021-06-25 v1
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 in \cite{DV} (arXiv:2007.12297).
Keywords
Cite
@article{arxiv.2106.13007,
title = {Bi-Lipschitz embeddings of quasiconformal trees},
author = {Guy C. David and Sylvester Eriksson-Bique and Vyron Vellis},
journal= {arXiv preprint arXiv:2106.13007},
year = {2021}
}
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14 pages