Boundary control in reconstruction of manifolds and metrics (the BC method)

One of the approaches to inverse problems based upon their relations to boundary control theory (the so-called BC method) is presented. The method gives an efficient way to reconstruct a Riemannian manifold via its response operator.(dynamical Dirichlet-to-Neumann map) or spectral data (a spectrum of the Beltrami-Laplace operator and traces of normal derivatives of the eigenfunctions). The approach is applied to the problem of recovering a density, including the case of inverse data given on part of a boundary. The results of the numerical testing are demonstrated.