Bi-Lipschitz geometry of quasiconformal trees

Autor:	David, Guy C., Vellis, Vyron
Rok vydání:	2020
Předmět:	Mathematics - Metric Geometry 30L05 30L10 (Primary) 05C05 51F99 (Secondary)
Druh dokumentu:	Working Paper
Popis:	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. We study the geometry of these trees in two directions. First, we construct a catalog of metric trees in a purely combinatorial way, and show that every quasiconformal tree is bi-Lipschitz equivalent to one of the trees in our catalog. This is inspired by results of Herron-Meyer and Rohde for quasi-arcs. Second, we show that a quasiconformal tree bi-Lipschitz embeds in a Euclidean space if and only if its set of leaves admits such an embedding. In particular, all quasi-arcs bi-Lipschitz embed into some Euclidean space. Comment: 40 pages. Added sections containing examples (Section 6) and a new result on spaces more general than trees (Section 7). Minor errors corrected and various clarifications added
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2007.12297 Zobrazit plný text záznamu View this record from Arxiv