6533b85cfe1ef96bd12bc1ab

RESEARCH PRODUCT

The non-Abelian X-ray transform on surfaces

Gabriel P. PaternainMikko Salo

subject

Mathematics - Differential GeometryMathematics - Analysis of PDEsDifferential Geometry (math.DG)FOS: MathematicsAnalysis of PDEs (math.AP)

description

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.

yearjournalcountryeditionlanguage
2020-06-03
http://arxiv.org/abs/2006.02257