English

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.

Keywords

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.)

R2 v1 2026-06-23T07:08:55.824Z