Vertical quasi-isometries and branched quasisymmetries

Autor:	Lindquist, Jeff, Pankka, Pekka
Rok vydání:	2019
Předmět:	Mathematics - Metric Geometry Mathematics - Complex Variables Primary 30L10 Secondary 30C65
Druh dokumentu:	Working Paper
Popis:	We introduce a class of mappings called vertical quasi-isometries and show that branched quasisymmetries $X\to Y$ of Guo and Williams between compact, bounded turning metric doubling spaces admit natural vertically quasi-isometric extensions $\widehat X\to \widehat Y$ between hyperbolic fillings $\widehat X$ and $\widehat Y$ of $X$ and $Y$, respectively. We also give a converse for this result by showing that a finite multiplicity vertical quasi-isometry $\widehat X \to \widehat Y$ between hyperbolic fillings induces a branched quasisymmetry $X \to Y$. Comment: 50 pages, 1 figure
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1911.12680 Zobrazit plný text záznamu View this record from Arxiv