1. Bi-Lipschitz embeddings of quasiconformal trees.
- Author
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David, Guy C., Eriksson-Bique, Sylvester, and Vellis, Vyron
- Subjects
- *
TREES , *MULTICASTING (Computer networks) , *MATHEMATICS , *DIAMETER - 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]. [ABSTRACT FROM AUTHOR]
- Published
- 2023
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