Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Scattering theory without injectivity radius assumptions and spectral
  stability for the Ricci flow   We prove a completely new integral criterion for the existence and
completeness of the wave operators $W_{\pm}(-\Delta_h,-\Delta_g, I_{g,h})$
corresponding to the (unique self-adjoint realizations of) the Laplace-Beltrami
operators $-\Delta_j$, $j=1,2$, that are induced by two quasi-isometric
complete Riemannian metrics $g$ and $h$ on an open manifold $M$. In particular,
this result provides a criterion for the absolutely continuous spectra of
$-\Delta_g$ and $-\Delta_h$ to coincide. Our proof relies on estimates that are
obtained using a probabilistic Bismut type formula for the gradient of a heat
semigroup. Unlike all previous results, our integral criterion only requires
some lower control on the Ricci curvatures and some upper control on the heat
kernels, but no control at all on the injectivity radii. As a consequence, we
obtain a stability result for the absolutely continuous spectrum under a Ricci
flow.

4
The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex
20
The categories of this paper are: acc-phys
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess
15
The categories of this paper are: nucl-ex
7
The categories of this paper are: hep-th
28
The categories of this paper are: alg-geom
22
The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an