Invertibility of local geodesic transverse and mixed ray transforms I: basic cases

2024/01/17 by Günther Uhlmann, Uhlmann, Gunther, Jian Zhai +1 · 1 citation
Engineering · Mathematics · Physics and Astronomy · #3D Shape Modeling and Analysis #53C22 #53C65 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.2401.09017

openalex publication_date 2024/01/17 · openalex created_date 2024/01/19 · openalex updated_date 2026/07/28

Abstract

Consider a compact Riemannian manifold in dimension n≥ 3 with strictly convex boundary. We show that the transverse ray transform of 1 tensors and the mixed ray transform of 1+1 tensors are invertible, up to natural obstructions, near a boundary point. When the manifold admits a strictly convex function, this local invertibility result leads to a global result by a layer stripping argument.

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