Vertical quasi-isometries and branched quasisymmetries

Jeff Lindquist; Pekka Pankka

doi:10.48550/arXiv.1911.12680

Vertical quasi-isometries and branched quasisymmetries

Research output: Contribution to journal › Article › Scientific

Abstract

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 $X \to Y$.

Original language	Other/Unknown
Journal	arXiv.org
ISSN	2331-8422
DOIs	https://doi.org/10.48550/arXiv.1911.12680
Publication status	Published - 28 Nov 2019
MoE publication type	B1 Journal article

Bibliographical note

50 pages, 1 figure

Fields of Science

math.MG
math.CV
Primary 30L10, Secondary 30C65

Access to Document

10.48550/arXiv.1911.12680Licence: Unspecified

Cite this

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title = "Vertical quasi-isometries and branched quasisymmetries",

abstract = " We introduce a class of mappings called vertical quasi-isometries and show that branched quasisymmetries \$X\textbackslash{}to Y\$ of Guo and Williams between compact, bounded turning metric doubling spaces admit natural vertically quasi-isometric extensions \$\textbackslash{}widehat X\textbackslash{}to \textbackslash{}widehat Y\$ between hyperbolic fillings \$\textbackslash{}widehat X\$ and \$\textbackslash{}widehat Y\$ of \$X\$ and \$Y\$, respectively. We also give a converse for this result by showing that a finite multiplicity vertical quasi-isometry \$\textbackslash{}widehat X \textbackslash{}to \textbackslash{}widehat Y\$ between hyperbolic fillings induces a branched quasisymmetry \$X \textbackslash{}to Y\$. ",

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AU - Pankka, Pekka

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N2 - 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 $X \to Y$.

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