Invariant distributions and the geodesic ray transform
Differential Geometry
2017-01-25 v2 Analysis of PDEs
Dynamical Systems
Abstract
We establish an equivalence principle between the solenoidal injectivity of the geodesic ray transform acting on symmetric -tensors and the existence of invariant distributions or smooth first integrals with prescribed projection over the set of solenoidal -tensors. We work with compact simple manifolds, but several of our results apply to non-trapping manifolds with strictly convex boundary.
Keywords
Cite
@article{arxiv.1511.04547,
title = {Invariant distributions and the geodesic ray transform},
author = {Gabriel P. Paternain and Hanming Zhou},
journal= {arXiv preprint arXiv:1511.04547},
year = {2017}
}
Comments
27 pages; final version, to appear in Analysis & PDE