Geodesic ray transform with matrix weights for piecewise constant functions
Differential Geometry
2020-10-23 v3
Abstract
We show injectivity of the geodesic X-ray transform on piecewise constant functions when the transform is weighted by a continuous matrix weight. The manifold is assumed to be compact and nontrapping of any dimension, and in dimension three and higher we assume a foliation condition. We make no assumption regarding conjugate points or differentiability of the weight. This extends recent results for unweighted transforms.
Cite
@article{arxiv.1901.03525,
title = {Geodesic ray transform with matrix weights for piecewise constant functions},
author = {Joonas Ilmavirta and Jesse Railo},
journal= {arXiv preprint arXiv:1901.03525},
year = {2020}
}
Comments
10 pages, 1 figure; accepted manuscript (to appear in Ann. Acad. Sci. Fenn. Math.)