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Bi-Lipschitz embeddings of quasiconformal trees

机译:Bi-Lipschitz embeddings of quasiconformal trees

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摘要

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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