Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On a classification of the gradient shrinking solitons   The main purpose of this article is to provide an alternate proof to a result
of Perelman on gradient shrinking solitons. In dimension three we also
generalize the result by removing the $\kappa$-non-collapsing assumption. In
high dimension this new method allows us to prove a classification result on
gradient shrinking solitons with vanishing Weyl curvature tensor, which
includes the rotationally symmetric ones.

17
The categories of this paper are: q-fin
12
The categories of this paper are: nucl-th
14
The categories of this paper are: math-ph
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph
1
The categories of this paper are: cs
15
The categories of this paper are: nucl-ex
11
The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
4
The categories of this paper are: cond-mat
16
The categories of this paper are: stat
34
The categories of this paper are: chem-ph
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin