Functions of constant geodesic x-ray transform. (29th May 2019) - Ilmavirta, Joonas; Paternain, Gabriel P
Abstract: We show that the existence of a function in L 1 with constant geodesic x-ray transform imposes geometrical restrictions on the manifold. The boundary of the manifold has to be umbilical and in the case of a strictly convex Euclidean domain, it must be a ball. Functions with constant geodesic x-ray transform always exist on manifolds with rotational symmetry.