Lagrangian Tori and Quantization Conditions Corresponding to Spectral Series of the Laplace Operator on a Surface of Revolution with Conical Points

详细

Semiclassical spectral series of the Laplace operator on a two-dimensional surface of revolution with a conical point are described. It is shown that in many cases asymptotic eigenvalues can be calculated from the quantization conditions on special Lagrangian tori, with the Maslov index of such tori being replaced by a real invariant expressed in terms of the cone apex angle.