Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: Critical points of inner functions, nonlinear partial differential
  equations, and an extension of Liouville's theorem
13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga
14
The categories of this paper are: math-ph
26
The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
23
The categories of this paper are: solv-int
25
The categories of this paper are: patt-sol
18
The categories of this paper are: econ
21
The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci
19
The categories of this paper are: eess
36
The categories of this paper are: cmp-lg
16
The categories of this paper are: stat