The Calderón problem for the conformal Laplacian
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 a conjecture in Lassas and Uhlmann (2002). We introduce a new coordinate system that replaces harmonic coordinates when determining the conformal class in a neighborhood of the boundary.
This is joint work with Matti Lassas and Mikko Salo.