3 papers
math.DG2013
On the range of the attenuated magnetic ray transform for connections and Higgs fields
Gareth Ainsworth, Yernat M. Assylbekov
For a two-dimensional simple magnetic system, we study the attenuated magnetic ray transform , with attenuation given by a unitary connection and a skew-Hermitian Higg…
math.DG2012
The Magnetic Ray Transform on Anosov Surfaces
Gareth Ainsworth
Assume (M,g,Ω) is a closed, oriented Riemannian surface equipped with an Anosov magnetic flow. We establish certain results on the surjectivity of the adjoint of the magnetic ray t…
math.DG2012
The Attenuated Magnetic Ray Transform on Surfaces
Gareth Ainsworth
It has been shown in [Pa1] that on a simple, compact Riemannian 2-manifold the attenuated geodesic ray transform, with attenuation given by a connection and Higgs field, is injecti…