Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Thurston boundary of the Teichm\"uller space is the space of big bang
  singularities of 2+1 gravity   The ADM formalism of vacuum general relativity in constant mean extrinsic
curvature spatial harmonic (CMCSH) gauge is used to study the asymptotic
behaviour of the solution curves of the dynamics of spacetimes of the
topological type $\Sigma_{g}\times \mathbb{R}$, $g>1$, where $\Sigma_{g}$ is a
closed Riemann surface of genus $g$. The configuration space of the gauge fixed
dynamics is identified with the Teichm\"uller space
($\mathcal{T}\Sigma_{g}\approx \mathbb{R}^{6g-6}$) of $\Sigma_{g}$. Utilizing
the properties of the Dirichlet energy of certain harmonic maps, estimates
derived from the associated elliptic equations in conjunction with a few
standard results of surface theory, we show that every non-trivial solution
curve runs off the edge of the Teichm\"uller space at the limit of the big bang
singularity and approaches the space of projective measured
laminations/foliations ($\mathcal{PML}$ $\mathcal{PMF}$), the Thurston boundary
of the Teichm\"uller space. This result which identifies the complete solution
space of the Einstein equations on flat spacetimes of the type
$\Sigma_{g}\times \mathbb{R}$, also yields yet another way to compactify the
Teichm\"uller space.

16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an
26
The categories of this paper are: bayes-an
20
The categories of this paper are: acc-phys
1
The categories of this paper are: cs
30
The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
18
The categories of this paper are: econ
12
The categories of this paper are: nucl-th
24
The categories of this paper are: dg-ga
17
The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin