P. Exner, M. Fraas
On geometric perturbations of critical Schr\"odinger 
operators with a surface interaction
(42K, LaTeX 2e)

ABSTRACT.  We study singular Schr\"odinger operators with an 
attractive interaction supported by a closed smooth surface $\man 
A\subset\mathbb{R}^3$ and analyze their behavior in the vicinity 
of the critical situation where such an operator has empty 
discrete spectrum and a threshold resonance. In particular, we 
show that if $\man A$ is a sphere and the critical coupling is 
constant over it, any sufficiently small smooth area preserving 
radial deformation 
gives rise to isolated eigenvalues. On the other hand, the 
discrete spectrum may be empty for general deformations. We also 
derive a related inequality for capacities associated with such 
surfaces.