Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rigidity of area-minimizing free boundary surfaces in mean convex
  three-manifolds   We prove a local splitting theorem for three-manifolds with mean convex
boundary and scalar curvature bounded from below that contain certain locally
area-minimizing free boundary surfaces. Our methods are based on those of
Micallef and Moraru. We use this local result to establish a global rigidity
theorem for area-minimizing free boundary disks. In the negative scalar
curvature case, this global result implies a rigidity theorem for solutions of
the Plateau problem with length-minimizing boundary.

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The categories of this paper are: q-alg
1
The categories of this paper are: cs
9
The categories of this paper are: nlin
26
The categories of this paper are: bayes-an
33
The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int
36
The categories of this paper are: cmp-lg
22
The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph
28
The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat