Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Maximum principle and convergence of fundamental solutions for the Ricci
  flow   In this paper we will prove a maximum principle for the solutions of linear
parabolic equation on complete non-compact manifolds with a time varying
metric. We will prove the convergence of the Neumann Green function of the
conjugate heat equation for the Ricci flow in $B_k\times (0,T)$ to the minimal
fundamental solution of the conjugate heat equation as $k\to\infty$. We will
prove the uniqueness of the fundamental solution under some exponential decay
assumption on the fundamental solution. We will also give a detail proof of the
convergence of the fundamental solutions of the conjugate heat equation for a
sequence of pointed Ricci flow $(M_k\times (-\alpha,0],x_k,g_k)$ to the
fundamental solution of the limit manifold as $k\to\infty$ which was used
without proof by Perelman in his proof of the pseudolocality theorem for Ricci
flow.

8
The categories of this paper are: hep-ex
11
The categories of this paper are: hep-lat
18
The categories of this paper are: econ
17
The categories of this paper are: q-fin
19
The categories of this paper are: eess
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
3
The categories of this paper are: physics
22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
34
The categories of this paper are: chem-ph