Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Scattering Theory and Spectral Stability under a Ricci Flow for Dirac
  Operators   Given a noncompact spin manifold $M$ with a fixed topological spin structure
and two complete Riemannian metrics $g$ and $h$ on $M$ with bounded sectional
curvatures, we prove a criterion for the existence and completeness of the wave
operators $\mathscr{W}_{\pm}(D_h, D_g, I_{g,h})$ and $\mathscr{W}_{\pm}(D_h^2,
D^2_g, I_{g,h})$, where $I_{g,h}$ is the canonically given unitary map between
the underlying $L^2$-spaces of spinors. This criterion does not involve any
injectivity radius assumptions and leads to a criterion for the stability of
the absolutely continuous spectrum of a Dirac operator and its square under a
Ricci flow.

22
The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph
34
The categories of this paper are: chem-ph
19
The categories of this paper are: eess
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The categories of this paper are: nlin
17
The categories of this paper are: q-fin
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The categories of this paper are: cmp-lg
23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
20
The categories of this paper are: acc-phys
7
The categories of this paper are: hep-th
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The categories of this paper are: bayes-an