Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Vertical quasi-isometries and branched quasisymmetries   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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The categories of this paper are: nlin
1
The categories of this paper are: cs
27
The categories of this paper are: comp-gas
21
The categories of this paper are: adap-org
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The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
22
The categories of this paper are: chao-dyn
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The categories of this paper are: q-bio
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The categories of this paper are: eess
3
The categories of this paper are: physics
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The categories of this paper are: math-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: dg-ga
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The categories of this paper are: cond-mat
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The categories of this paper are: quant-ph
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The categories of this paper are: funct-an