Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Mean curvature and compactification of surfaces in a negatively curved
  Cartan-Hadamard manifold   We state and prove a Chern-Osserman-type inequality in terms of the volume
growth for complete surfaces with controlled mean curvature properly immersed
in a Cartan-Hadamard manifold $N$ with sectional curvatures bounded from above
by a negative quantity $K_{N}\leq b<0$

22
The categories of this paper are: chao-dyn
29
The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
19
The categories of this paper are: eess
8
The categories of this paper are: hep-ex
6
The categories of this paper are: astro-ph
34
The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an
14
The categories of this paper are: math-ph
17
The categories of this paper are: q-fin
7
The categories of this paper are: hep-th
37
The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio
21
The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom