The geodesic ray transform on two-dimensional Cartan-Hadamard manifolds
  We prove two injectivity theorems for the geodesic ray transform on two-dimensional, complete, simply connected Riemannian manifolds with non-positive Gaussian curvature, also known as Cartan-Hadamard manifolds. The first theorem is concerned with bounded non-positive curvature and the second with decaying non-positive curvature. 
Jere Lehtonen
math.DG