2024/11/03 by Sebastián Muñoz-Thon, Muñoz-Thon, Sebastián · 1 citation
Computer Science · Engineering · Mathematics · #35J25 #35R30 #58E20 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Analysis Techniques #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.2411.01659
openalex publication_date 2024/11/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study a version of Calderón's problem for harmonic maps between Riemannian manifolds. By using the higher linearization method, we first show that the Dirichlet-to-Neumann map determines the metric on the domain up to a natural gauge in three cases: on surfaces, on analytic manifolds, and in conformally transversally anisotropic manifolds on a fixed conformal class with injective ray transform on the transversal manifold. Next, using higher linearizations we obtain integral identities that allows us to show that the metrics on the target have the same jets at one point. In particular, if the target is analytic, the metrics are equal. We also prove an energy rigidity result, in the sense that the Dirichlet energies of harmonic maps determines the Dirichlet-to-Neumann map.