The spectrum and the eigenbasis of the Laplace–Beltrami operator on the suspensions of toric automorphisms are investigated. A description in terms of solutions of one-dimensional Schrödinger’s equation is presented. Bibliography: 10 titles. §

The governing equations of three dimensional elasticity problems include the six Beltrami-Michell stress compatibility equations, the three differential equations of equilibrium, and the six material constitutive relations; and these are usually solved subject to the boundary conditions. The system of fifteen differential equations is usually difficult to solve, and simplified methods are usual...

We prove a purely algebraic version of an eigenvalue inequality of Hile and Protter, and derive corollaries bounding diierences of eigenvalues of Laplace{ Beltrami operators on manifolds. We signiicantly improve earlier bounds of

We adapt in the present note the perturbation method introduced in [3] to get a lower Gaussian bound for the Neumann heat kernel of the Laplace-Beltrami operator on an open subset of a compact Riemannian manifold.