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The X-ray transform for connections in negative curvature
(SpringerCommunications in Mathematical Physics, 2015-11-23)
We consider integral geometry inverse problems for unitary connections and skew-Hermitian Higgs fields on manifolds with negative sectional curvature. The results apply to manifolds in any dimension, with or without boundary, ...
Invariant distributions, Beurling transforms and tensor tomography in higher dimensions
(SpringerMathematische Annalen, 2015-02-01)
In the recent articles [PSU13, PSU14c], a number of tensor tomography results were proved on two-dimensional manifolds. The purpose of this paper is to extend some of these methods to manifolds of any dimension. A central ...