Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Grafting rays fellow travel Teichmuller geodesics   Given a measured geodesic lamination on a hyperbolic surface, grafting the
surface along multiples of the lamination defines a path in Teichmuller space,
called the grafting ray. We show that every grafting ray, after
reparametrization, is a Teichmuller quasi-geodesic and stays in a bounded
neighborhood of a Teichmuller geodesic.
  As part of our approach, we show that grafting rays have controlled
dependence on the starting point. That is, for any measured geodesic lamination
Lambda, the map of Teichmuller space which is defined by grafting along Lambda
is L-Lipschitz with respect to the Teichmuller metric, where L is a universal
constant. This Lipschitz property follows from an extension of grafting to an
open neighborhood of Teichmuller space in the space of quasi-Fuchsian groups.

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The categories of this paper are: dg-ga
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
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The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
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The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics
0
The categories of this paper are: hep-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: eess
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The categories of this paper are: solv-int
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The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat