Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rigidity of area-minimizing hyperbolic surfaces in three-manifolds   We prove that if $M$ is a three-manifold with scalar curvature greater than
or equal to -2 and $\Sigma\subset M$ is a two-sided compact embedded Riemann
surface of genus greater than 1 which is locally area-minimizing, then the area
of $\Sigma$ is greater than or equal to $4\pi(g(\Sigma)-1)$, where $g(\Sigma)$
denotes the genus of $\Sigma$. In the equality case, we prove that the induced
metric on $\Sigma$ has constant Gauss curvature equal to -1 and locally $M$
splits along $\Sigma$. As a corollary, we obtain a rigidity result for
cylinders $(I\times\Sigma,dt^2+g_{\Sigma})$, where $I=[a,b]\subset\mathbb{R}$
and $g_{\Sigma}$ is a Riemannian metric on $\Sigma$ with constant Gauss
curvature equal to -1.

22
The categories of this paper are: chao-dyn
7
The categories of this paper are: hep-th
27
The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
19
The categories of this paper are: eess
10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc
4
The categories of this paper are: cond-mat