Gap estimates for Schrödinger operators depending on curvature

Evans Harrell Georgia Tech

Schrödinger operators depending on curvature, of the form

−∇^{2} + q(κ)

on L^{2}(M), where M is a compact surface or submanifold of R^{n} arise in the study of thin structures, among other topics in physics. Typically, q is a quadratic function of the principal curvatures. The author will present some estimates of the low-lying eigenvalues and the gaps between them. In some cases these estimates are shown to be optimal.