Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Any isometry between the spheres of absolutely smooth $2$-dimensional
  Banach spaces is linear   We prove that any isometry between the unit spheres of $C^2$-smooth (more
generally, absolutely smooth) smooth Banach spaces extends to a linear isometry
of the Banach spaces. This answers the famous Tingley's problem in the class of
absolutely smooth $2$-dimensional Banach spaces.

6
The categories of this paper are: astro-ph
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The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga
1
The categories of this paper are: cs
22
The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex
25
The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
0
The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
26
The categories of this paper are: bayes-an
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The categories of this paper are: hep-lat