Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Scattering theory for Riemannian Laplacians   In this paper we introduce a notion of scattering theory for the
Laplace-Beltrami operator on non-compact, connected and complete Riemannian
manifolds. A principal condition is given by a certain positive lower bound of
the second fundamental form of angular submanifolds at infinity. Another
condition is certain bounds of derivatives up to order one of the trace of this
quantity. These conditions are shown to be optimal for existence and
completeness of a wave operator. Our theory does not involve prescribed
asymptotic behaviour of the metric at infinity (like asymptotic Euclidean or
hyperbolic metrics studied previously in the literature). A consequence of the
theory is spectral theory for the Laplace-Beltrami operator including
identification of the continuous spectrum and absence of singular continuous
spectrum.

31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
20
The categories of this paper are: acc-phys
13
The categories of this paper are: quant-ph
16
The categories of this paper are: stat
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org
24
The categories of this paper are: dg-ga
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol
34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex