2025/12/22 by Seán Gomes, Lauri Oksanen, Gomes, Sean +1
Mathematics · Physics and Astronomy · #35R30 #Advanced Differential Geometry Research #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds
paper · doi:10.48550/arxiv.2512.19601
openalex publication_date 2025/12/22 · openalex created_date 2025/12/24 · openalex updated_date 2026/07/28
In this paper we study a Lorentzian version of the Calderón problem, which is concerned with the determination of a connection and potential on a Hermitian vector bundle over a Lorentzian manifold from the Dirichlet-to-Neumann map of the associated connection wave operator. For a class of Lorentzian manifolds satisfying a curvature bound, including perturbations of Minkowski space over strictly convex domains, the connection and potential is shown to be uniquely determined up to the natural gauge transformations of the problem. The proof is based on ideas from the earlier works arXiv:2008.07508, arXiv:2112.01663 of the second author in the scalar setting.