Search
Now showing items 1-4 of 4
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 ...
INVARIANT DISTRIBUTIONS AND THE GEODESIC RAY TRANSFORM
(Mathematical Science PublishersAnalysis & PDE, 2016-12-11)
We establish an equivalence principle between the solenoidal injectivity of the geodesic ray transform acting on symmetric $\textit{m}$-tensors and the existence of invariant distributions or smooth first integrals with ...
The geodesic X-ray transform with a $GL(n,\mathbb{C})$-connection
We derive reconstruction formulas for a family of geodesic ray transforms with connection, defined on simple Riemannian surfaces. Such formulas provide injectivity of such all transforms in a neighbourhood of constant ...