Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A simple proof on the non-existence of shrinking breathers for the Ricci
  flow   Suppose $M$ is a compact n-dimensional manifold, $n\ge 2$, with a metric
$g_{ij}(x,t)$ that evolves by the Ricci flow $\partial_tg_{ij}=-2R_{ij}$ in
$M\times (0,T)$. We will give a simple proof of a recent result of Perelman on
the non-existence of shrinking breather without using the logarithmic Sobolev
inequality.

36
The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
18
The categories of this paper are: econ
22
The categories of this paper are: chao-dyn
33
The categories of this paper are: plasm-ph
19
The categories of this paper are: eess
27
The categories of this paper are: comp-gas
12
The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys
23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th
14
The categories of this paper are: math-ph
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg