Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Time-dependent Sobolev inequality along the Ricci flow   In this article we get a time-dependent Sobolev inequality along the Ricci
flow which generalizes the earlier results of Zhang, Ye, Hsu. As an application
of the time-dependent Sobolev inequality, we also get a growth of the ratio of
bob-collapsing along the Ricci flow.

23
The categories of this paper are: solv-int
15
The categories of this paper are: nucl-ex
5
The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys
4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
1
The categories of this paper are: cs
6
The categories of this paper are: astro-ph
14
The categories of this paper are: math-ph
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
19
The categories of this paper are: eess
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin