Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Li-Yau gradient bounds on compact manifolds under nearly optimal
  curvature conditions   We prove Li-Yau type gradient bounds for the heat equation either on
manifolds with fixed metric or under the Ricci flow. In the former case the
curvature condition is $|Ric^-| \in L^p$ for some $p>n/2$, or $\sup_\M \int_\M
|Ric^-|^2(y)d^{2-n}(x,y)dy<\infty$, where $n$ is the dimension of the manifold.
In the later case, one only needs scalar curvature being bounded. We will
explain why the conditions are nearly optimal and give an application. The
Li-Yau bound for the heat equation on manifolds with fixed metric seems to be
the first one allowing Ricci curvature not bounded from below.

25
The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
20
The categories of this paper are: acc-phys
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn
24
The categories of this paper are: dg-ga
1
The categories of this paper are: cs
5
The categories of this paper are: gr-qc
23
The categories of this paper are: solv-int