The non-Abelian X-ray transform on surfaces
Differential Geometry
2022-01-27 v2 Analysis of PDEs
Abstract
This paper settles the question of injectivity of the non-Abelian X-ray transform on simple surfaces for the general linear group of invertible complex matrices. The main idea is to use a factorization theorem for Loop Groups to reduce to the setting of the unitary group, where energy methods and scalar holomorphic integrating factors can be used. We also show that our main theorem extends to cover the case of an arbitrary Lie group.
Keywords
Cite
@article{arxiv.2006.02257,
title = {The non-Abelian X-ray transform on surfaces},
author = {Gabriel P. Paternain and Mikko Salo},
journal= {arXiv preprint arXiv:2006.02257},
year = {2022}
}
Comments
16 pages, this version to appear in JDG