Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the global evolution problem in 2+1 gravity   Existence of global CMC foliations of constant curvature 3-dimensional
maximal globally hyperbolic Lorentzian manifolds, containing a constant mean
curvature hypersurface with $\genus(\Sigma) > 1$ is proved. Constant curvature
3-dimensional Lorentzian manifolds can be viewed as solutions to the 2+1 vacuum
Einstein equations with a cosmological constant. The proof is based on the
reduction of the corresponding Hamiltonian system in constant mean curvature
gauge to a time dependent Hamiltonian system on the cotangent bundle of
Teichm\"uller space. Estimates of the Dirichlet energy of the induced metric
play an essential role in the proof.

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The categories of this paper are: physics
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The categories of this paper are: cond-mat
1
The categories of this paper are: cs
10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex
26
The categories of this paper are: bayes-an
31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
29
The categories of this paper are: funct-an
19
The categories of this paper are: eess
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The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org
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The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
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The categories of this paper are: hep-ph