Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Closed geodesics on incomplete surfaces   We consider the problem of finding embedded closed geodesics on the
two-sphere with an incomplete metric defined outside a point. Various
techniques including curve shortening methods are used.

28
The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph
17
The categories of this paper are: q-fin
32
The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
3
The categories of this paper are: physics
13
The categories of this paper are: quant-ph
16
The categories of this paper are: stat