On the s-injectivity of the X-ray transform on manifolds with hyperbolic trapped set
Analysis of PDEs
2019-08-08 v3 Differential Geometry
Dynamical Systems
Abstract
For smooth compact connected manifolds with strictly convex boundary, no conjugate points and a hyperbolic trapped set, we prove an equivalence principle concerning the injectivity of the X-ray transform on symmetric solenoidal tensors and the surjectivity of an operator on the set of solenoidal tensors. This allows us to establish the injectivity of the X-ray transform on solenoidal tensors of any order in the case of a surface satisfying these assumptions.
Cite
@article{arxiv.1807.03680,
title = {On the s-injectivity of the X-ray transform on manifolds with hyperbolic trapped set},
author = {Thibault Lefeuvre},
journal= {arXiv preprint arXiv:1807.03680},
year = {2019}
}
Comments
24 pages, 2 figures. Theorem 1.2 improved thanks to a referee's suggestion: the condition "I^e_m is s-injective" is relaxed to "I_m is s-injective"