2019/09/04 by Thierry Daudé, Niky Kamran, Daudé, Thierry +3
Mathematics · #Analysis of PDEs (math.AP) #Analytic and geometric function theory #FOS: Mathematics #FOS: Physical sciences #Geometric Analysis and Curvature Flows #Mathematical Physics (math-ph) #Numerical methods in inverse problems #Spectral Theory (math.SP)
paper · doi:10.48550/arxiv.1909.01669
openalex publication_date 2019/09/04 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28
Conformally Stäckel manifolds can be characterized as the class of n-dimensional pseudo-Riemannian manifolds (M, G) on which the Hamilton-Jacobi equation G(∇u, ∇u) = 0 for null geodesics and the Laplace equation --Δ G ψ = 0 are solvable by R-separation of variables. In the particular case in which the metric has Riemannian signature, they provide explicit examples of metrics admitting a set of n--1 commuting conformal symmetry operators for the Laplace-Beltrami operator Δ G. In this paper, we solve the anisotropic Calderón problem on compact 3-dimensional Riemannian manifolds with boundary which are conformally Stäckel, that is we show that the metric of such manifolds is uniquely determined by the Dirichlet-to-Neumann map measured on the boundary of the manifold, up to dieomorphims that preserve the boundary.