Edge and Curvature Effects in Weyl's Problem

It is shown that the edge and curvature effects in the asymptotic distribution of the eigenvalues of the Laplace operator ${\nabla }^2$ for a cylindrical domain, studied recently by Baltes, arise from a common origin and can be obtained directly from Fedosov's formula for a polyhedron. Generalization to arbitrary domains (with pure boundary conditions) and to cylindrical domains (with mixed boundary conditions) is presented. The latter results substantiate certain conjectures made previously by one of the authors.