Functions of constant geodesic X-ray transform
Differential Geometry
2019-09-04 v2 Classical Analysis and ODEs
Abstract
We show that the existence of a function in 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.
Cite
@article{arxiv.1812.03515,
title = {Functions of constant geodesic X-ray transform},
author = {Joonas Ilmavirta and Gabriel P. Paternain},
journal= {arXiv preprint arXiv:1812.03515},
year = {2019}
}
Comments
10 pages