Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Boundary at Infinity of the Curve Complex and the Relative
  Teichm\"{u}ller Space   In this paper we study the boundary at infinity of the curve complex
$\mathcal{C}(S)$ of a surface $S$ of finite type and the relative
Teichm\"{u}ller space $\mathcal{T}_{el}(S)$ obtained from the Teichm\"{u}ller
space by collapsing each region where a simple closed curve is short to be a
set of diameter 1. $\mathcal{C}(S)$ and $\mathcal{T}_{el}(S)$ are
quasi-isometric, and Masur-Minsky have shown that $\mathcal{C}(S)$ and
$\mathcal{T}_{el}(S)$ are hyperbolic in the sense of Gromov. We show that the
boundary at infinity of $\mathcal{C}(S)$ and $\mathcal{T}_{el}(S)$ is the space
of topological equivalence classes of minimal foliations on $S$.

29
The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
19
The categories of this paper are: eess
26
The categories of this paper are: bayes-an
22
The categories of this paper are: chao-dyn
13
The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
16
The categories of this paper are: stat
14
The categories of this paper are: math-ph
27
The categories of this paper are: comp-gas
11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
23
The categories of this paper are: solv-int