Stability and Reconstruction in Gel'fand Inverse Boundary Spectral   Problem
  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. 
Atsushi Katsuda and Yaroslav Kurylev and Matti Lassas