Abstract:
We discuss the discrete spectrum of Schroedinger operators with an attractive
singular interaction supported by a curve or surface in R^n, n=2,3. Asymptotic
expansions for the number of negative eigenvalues are derived as well as
expansions for the j-th eigenvalue which is expressed in terms of a comparison
operator with the potential determined by the geometry of the manifold. We also
discuss the behaviour of band spectrum for periodic manifolds and list some
open problems.