2016/12/23 by Matti Lassas, Lassas, Matti, Tony Liimatainen +3 · 2 citations
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT) #Nonlinear Partial Differential Equations #Numerical methods in inverse problems
paper · pdf · doi:10.48550/arxiv.1612.07939
openalex publication_date 2016/12/23 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28
We consider a conformally invariant version of the Calderón problem, where the objective is to determine the conformal class of a Riemannian manifold with boundary from the Dirichlet-to-Neumann map for the conformal Laplacian. The main result states that a locally conformally real-analytic manifold in dimensions ≥ 3 can be determined in this way, giving a positive answer to an earlier conjecture by Lassas and Uhlmann (2001). The proof proceeds as in the standard Calderón problem on a real-analytic Riemannian manifold, but new features appear due to the conformal structure. In particular, we introduce a new coordinate system that replaces harmonic coordinates when determining the conformal class in a neighborhood of the boundary.