Bi-Lipschitz embeddings of quasiconformal trees
David, Guy; Eriksson-Bique, Sylvester; Vellis, Vyron (2023-02-02)
American mathematical society
02.02.2023
David, G., Eriksson-Bique, S., & Vellis, V. (2023). Bi-Lipschitz embeddings of quasiconformal trees. Proceedings of the American Mathematical Society, 151, 2031-2044. https://doi.org/10.1090/proc/16252
https://creativecommons.org/licenses/by/4.0/
© 2023 by the authors. This manuscript version is made available under the CC-BY 4.0 license https://creativecommons.org/licenses/by/4.0/
https://creativecommons.org/licenses/by/4.0/
© 2023 by the authors. This manuscript version is made available under the CC-BY 4.0 license https://creativecommons.org/licenses/by/4.0/
https://creativecommons.org/licenses/by/4.0/
Julkaisun pysyvä osoite on
https://urn.fi/URN:NBN:fi:oulu-202312153869
https://urn.fi/URN:NBN:fi:oulu-202312153869
Tiivistelmä
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].
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].
Kokoelmat
- Avoin saatavuus [37887]
Ellei muuten mainita, aineiston lisenssi on https://creativecommons.org/licenses/by/4.0/