Semiclassical Asymptotic Behavior of the Spectrum of a Nonselfadjoint Elliptic Operator on a Two-Dimensional Surface of Revolution

The asymptotics as ɛ → 0 of the spectrum of the shifted Laplace operator H = ɛΔ + ∂v on a two-dimensional compact surface of revolution homeomorphic to the sphere is described, where v is a vector field.