Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spectral estimates for Riemannian submersions with fibers of basic mean
  curvature   For Riemannian submersions with fibers of basic mean curvature, we compare
the spectrum of the total space with the spectrum of a Schr\"{o}dinger operator
on the base manifold. Exploiting this concept, we study submersions arising
from actions of Lie groups. In this context, we extend the state of the art
results on the bottom of the spectrum under Riemannian coverings. As an
application, we compute the bottom of the spectrum and the Cheeger constant of
connected, amenable Lie groups.

8
The categories of this paper are: hep-ex
17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
16
The categories of this paper are: stat
29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
20
The categories of this paper are: acc-phys
19
The categories of this paper are: eess
18
The categories of this paper are: econ
23
The categories of this paper are: solv-int
5
The categories of this paper are: gr-qc
32
The categories of this paper are: atom-ph
27
The categories of this paper are: comp-gas