American Institute of Mathematical Sciences

February  2013, 7(1): 27-46. doi: 10.3934/ipi.2013.7.27

The attenuated magnetic ray transform on surfaces

 1 Trinity College, Cambridge, CB2 1TQ, United Kingdom

Received  June 2012 Revised  October 2012 Published  February 2013

It has been shown in [10] that on a simple, compact Riemannian 2-manifold the attenuated geodesic ray transform, with attenuation given by a connection and Higgs field, is injective on functions and 1-forms modulo the natural obstruction. Furthermore, the scattering relation determines the connection and Higgs field modulo a gauge transformation. We extend the results obtained therein to the case of magnetic geodesics. In addition, we provide an application to tensor tomography in the magnetic setting, along the lines of [11].
Citation: Gareth Ainsworth. The attenuated magnetic ray transform on surfaces. Inverse Problems & Imaging, 2013, 7 (1) : 27-46. doi: 10.3934/ipi.2013.7.27
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References:
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