Riemannian and Lorentzian Calderón problem under Magnetic Perturbation

2025/05/21 by Yuchao Yi, Yi, Yuchao · 1 citation
Earth and Planetary Sciences · Mathematics · Physics and Astronomy · #35J25 #35L20 #35R30 (Primary) #53C50 #58J32 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geophysics and Gravity Measurements #Numerical methods in inverse problems #Statistical Mechanics and Entropy

paper · pdf · doi:10.48550/arxiv.2505.15189

openalex publication_date 2025/05/21 · openalex created_date 2025/10/19 · openalex updated_date 2026/07/28

Abstract

We study both the Riemannian and Lorentzian Calderón problem when a family of Dirichlet-to-Neumann maps are given for an open set of magnetic/electromagnetic potentials. For the Riemannian version, by allowing small perturbations of the magnetic potential, we use the Runge Approximation Theorem to show that the metric can be uniquely determined. There is no gauge equivalence in this case. For the Lorentzian version, we use microlocal analysis to construct the trajectory of null-geodesics via generic perturbations of the electromagnetic potential, hence the conformal class of the metric can be constructed. Moreover, we also show, in the Lorentzian case, the same result can be obtained using generic perturbations of the metric itself.

Citations

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Cited by

• The Dirichlet-to-Neumann map on asymptotically anti-de Sitter spaces and holography

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