Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Checking real analyticity on surfaces   We prove that a real-valued function (that is not assumed to be continuous)
on a real analytic manifold is analytic whenever all its restrictions to
analytic submanifolds homeomorphic to the 2-sphere are analytic. This is a real
analog for the classical theorem of Hartogs that a function on a complex
manifold is complex analytic iff it is complex analytic when restricted to any
complex curve.

23
The categories of this paper are: solv-int
24
The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
18
The categories of this paper are: econ
29
The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
20
The categories of this paper are: acc-phys
7
The categories of this paper are: hep-th
14
The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph