Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stability of the non-abelian $X$-ray transform in dimension $\ge 3$   Non-abelian $X$-ray tomography seeks to recover a matrix potential
$\Phi:M\rightarrow \mathbb{C}^{m\times m}$ in a domain $M$ from measurements of
its so called scattering data $C_\Phi$ at $\partial M$. For $\dim M\ge 3$ (and
under appropriate convexity and regularity conditions), injectivity of the
forward map $\Phi \mapsto C_\Phi$ was established in [arXiv:1605.07894]. In
this article we extend [arXiv:1605.07894] by proving a H\"older-type stability
estimate. As an application we generalise a statistical consistency result for
$\dim M =2$ [arXiv:1905.00860] to higher dimensions. The injectivity proof in
[arXiv:1605.07894] relies on a novel method by Uhlmann-Vasy [arXiv:1210.2084],
which first establishes injectivity in a shallow layer below $\partial M$ and
then globalises this by a layer stripping argument. The main technical
contribution of this paper is a more quantitative version of these arguments,
in particular proving uniform bounds on layer-depth and stability constants.

21
The categories of this paper are: adap-org
29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph
19
The categories of this paper are: eess
6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
11
The categories of this paper are: hep-lat
15
The categories of this paper are: nucl-ex
18
The categories of this paper are: econ
7
The categories of this paper are: hep-th