Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the essential spectrum of the Laplacian and the drifted Laplacian   This paper concerns the $L^2$ essential spectrum of the Laplacian $\Delta$
and the drift Laplacian $\Delta_f$ on complete Riemannian manifolds endowed
with a weighted measure $e^{-f}d\;vol_g$. We prove that the essential spectrum
of the drift Laplacian $\Delta_f$ is $[0,+\infty) $ provided the Bakry-\'Emery
curvature tensor $Ric_f$ is nonnegative and $f$ has sublinear growth . When
$Ric_f \geq 1/2 g$ and $|\nabla f|^2 \leq f$, we show that the essential
spectrum of the Laplacian is also $[0,+\infty)$. During the proofs of these
results, the $f$-volume growth estimate plays an important role and may be of
independent interest.

1
The categories of this paper are: cs
27
The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph