Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Free boundary constant mean curvature surfaces in a strictly convex
  three-manifold   Let $C$ be a strictly convex domain in a $3$-dimensional Riemannian manifold
with sectional curvature bounded above by a constant and let $\Sigma$ be a
constant mean curvature surface with free boundary in $C$. We provide a
pinching condition on the length of the traceless second fundamental form on
$\Sigma$ which guarantees that the surface is homeomorphic to either a disk or
an annulus. Furthermore, under the same pinching condition, we prove that if
$C$ is a geodesic ball of $3$-dimensional space forms, then $\Sigma$ is either
a spherical cap or a Delaunay surface.

3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
19
The categories of this paper are: eess
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
23
The categories of this paper are: solv-int
34
The categories of this paper are: chem-ph
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The categories of this paper are: gr-qc
26
The categories of this paper are: bayes-an
28
The categories of this paper are: alg-geom
1
The categories of this paper are: cs
6
The categories of this paper are: astro-ph
14
The categories of this paper are: math-ph