Bound states due to a strong δ interaction supported by a curved surface

We study the Schrodinger operator -Delta-alphadelta(x-Gamma) in L-2(R-3) with a delta interaction supported by an infinite non-planar surface Gamma which is smooth and admits a global normal parametrization with a uniformly elliptic metric. We show that if Gamma is asymptotically planar in a suitable sense and alpha > 0 is sufficiently large, this operator has a non-empty discrete spectrum and derive an asymptotic expansion of the eigenvalues in terms of a `two-dimensional' comparison operator determined by the geometry of the surface Gamma.