Invertibility of local geodesic transverse and mixed ray transforms II: higher order tensors

Gunther Uhlmann; Jian Zhai

Invertibility of local geodesic transverse and mixed ray transforms II: higher order tensors

Differential Geometry 2024-02-21 v1

Authors: Gunther Uhlmann , Jian Zhai

Abstract

Consider a compact Riemannian manifold in dimension $n$ with strictly convex boundary. We show the local invertibility near a boundary point of the transverse ray transform of $2$ tensors for $n\geq 3$ and the mixed ray transform of $2+2$ tensors for $n=3$ . When the manifold admits a strictly convex function, this local invertibility result leads to global invertibility.

Keywords

ray transform transverse ray transform mixed ray transform Riemannian manifold tensor fields local invertibility global invertibility

Cite

@article{arxiv.2402.12640,
  title  = {Invertibility of local geodesic transverse and mixed ray transforms II: higher order tensors},
  author = {Gunther Uhlmann and Jian Zhai},
  journal= {arXiv preprint arXiv:2402.12640},
  year   = {2024}
}

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