Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The heat trace for the drifting Laplacian and Schr\"odinger operators on
  manifolds   We study the heat trace for both the drifting Laplacian as well as
Schr\"odinger operators on compact Riemannian manifolds. In the case of a
finite regularity potential or weight function, we prove the existence of a
partial (six term) asymptotic expansion of the heat trace for small times as
well as a suitable remainder estimate. We also demonstrate that the more
precise asymptotic behavior of the remainder is determined by and conversely
distinguishes higher (Sobolev) regularity on the potential or weight function.
In the case of a smooth weight function, we determine the full asymptotic
expansion of the heat trace for the drifting Laplacian for small times. We then
use the heat trace to study the asymptotics of the eigenvalue counting
function. In both cases the Weyl law coincides with the Weyl law for the
Riemannian manifold with the standard Laplace-Beltrami operator. We conclude by
demonstrating isospectrality results for the drifting Laplacian on compact
manifolds.

9
The categories of this paper are: nlin
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
25
The categories of this paper are: patt-sol
19
The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
35
The categories of this paper are: mtrl-th
1
The categories of this paper are: cs
18
The categories of this paper are: econ
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio