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

Fuente: arXiv
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Hauptverfasser: Uhlmann, Gunther, Zhai, Jian
Format: Preprint
Veröffentlicht: 2024
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author Uhlmann, Gunther
Zhai, Jian
author_facet Uhlmann, Gunther
Zhai, Jian
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2402_12640
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Invertibility of local geodesic transverse and mixed ray transforms II: higher order tensors
Uhlmann, Gunther
Zhai, Jian
Differential Geometry
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.
title Invertibility of local geodesic transverse and mixed ray transforms II: higher order tensors
topic Differential Geometry
url https://arxiv.org/abs/2402.12640