Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Differential Harnack inequalities on Riemannian manifolds I : linear
  heat equation   In the first part of this paper, we get new Li-Yau type gradient estimates
for positive solutions of heat equation on Riemmannian manifolds with
$Ricci(M)\ge -k$, $k\in \mathbb R$. As applications, several parabolic Harnack
inequalities are obtained and they lead to new estimates on heat kernels of
manifolds with Ricci curvature bounded from below. In the second part, we
establish a Perelman type Li-Yau-Hamilton differential Harnack inequality for
heat kernels on manifolds with $Ricci(M)\ge -k$, which generalizes a result of
L. Ni \cite{NL1,NL4}. As applications, we obtain new Harnack inequalities and
heat kernel estimates on general manifolds. We also obtain various entropy
monotonicity formulas for all compact Riemannian manifolds.

29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ
19
The categories of this paper are: eess
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
27
The categories of this paper are: comp-gas
25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg
15
The categories of this paper are: nucl-ex
5
The categories of this paper are: gr-qc
17
The categories of this paper are: q-fin