| Abstract: |
| In this talk I will discuss the invertibility of the geodesic X-ray
transform on one forms and 2-tensors on asymptotically conic
manifolds, up to the natural obstruction, allowing existence of
certain kinds of conjugate points. We use the 1-cusp
pseudodifferential operator algebra and its semiclassical foliation
version introduced and used by Vasy and Zachos, who showed the same type
invertibility on functions.
The complication of the invertibility of the tensorial X-ray
transform, compared with X-ray transform on functions, is caused by
the natural kernel of the transform consisting of `potential
tensors`. We overcome this by arranging a modified solenoidal gauge condition,
under which we have the invertibility of the X-ray transform.
This can be considered as a linearized version
of the boundary rigidity problem. |
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