Symmetry from sectional integrals for convex domains

Functions of constant geodesic x-ray transform

“…With a slicing argument as the one used for theorem 11, one should be able to generalize the result further to any d-plane Radon transform. It was indeed recently verified [4] that if the Radon transform depends only on the distance of the hyperplane to the nearest parallel hyperplane tangent to the boundary, then the domain has to be a ball. No integrable function has constant Radon transform in R n for n ≥ 3.…”