Functions of constant geodesic x-ray transform. (29th May 2019)

• Record Type: Journal Article
• Authors: Ilmavirta, Joonas; Paternain, Gabriel P
• Is Part Of: Inverse problems. Volume 35:Number 6(2019)
• Publication Date: 2019-05-29
• Subjects: x-ray transform -- range analysis -- integral geometry -- inverse problems; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/ab0b6f
• Languages: English
• ISSNs: 0266-5611

Abstract

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.