Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Convergence of the Ricci flow toward a unique soliton   We will consider a {\it $\tau$-flow}, given by the equation
$\frac{d}{dt}g_{ij} = -2R_{ij} + \frac{1}{\tau}g_{ij}$ on a closed manifold
$M$, for all times $t\in [0,\infty)$. We will prove that if the curvature
operator and the diameter of $(M,g(t))$ are uniformly bounded along the flow
and if one of the limit solitons is integrable, then we have a convergence of
the flow toward a unique soliton, up to a diffeomorphism.

23
The categories of this paper are: solv-int
20
The categories of this paper are: acc-phys
4
The categories of this paper are: cond-mat
29
The categories of this paper are: funct-an
34
The categories of this paper are: chem-ph
1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph
17
The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th
15
The categories of this paper are: nucl-ex
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th