Stability and Reconstruction in Gel'fand Inverse Boundary Spectral Problem

Atsushi Katsuda, Yaroslav Kurylev, and Matti Lassas

We consider stability and approximate reconstruction of Riemannian manifold when the finite number of eigenvalues of the Laplace-Beltrami operator and the boundary values of the corresponding eigenfunctions are given. The reconstruction can be done in stable way when manifold is a priori known to satisfy natural geometrical conditions related to curvature and other invariant quantities.