Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Long-time behavior of 3 dimensional Ricci flow -- D: Proof of the main
  results   This is the fourth and last part of a series of papers on the long-time
behavior of 3 dimensional Ricci flows with surgery. In this paper, we prove our
main two results. The first result states that if the surgeries are performed
correctly, then the flow becomes non-singular eventually and the curvature is
bounded by $C t^{-1}$. The second result provides a qualitative description of
the geometry as $t \to \infty$.

31
The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph
14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
16
The categories of this paper are: stat
21
The categories of this paper are: adap-org
17
The categories of this paper are: q-fin
1
The categories of this paper are: cs
22
The categories of this paper are: chao-dyn