English

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 L1L^{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.

Keywords

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

R2 v1 2026-06-23T06:36:45.240Z