Discreteness of the spectrum of the Laplace-Beltrami operator
arXiv:math/0701564 · doi:10.1007/s12220-008-9055-6
Abstract
We propose simple conditions equivalent to the discreteness of the spectrum of the Laplace-Beltrami operator on a class of Riemannian manifolds close to warped products. For this class of manifolds we establish a relationship between discreteness of the spectrum and stochastic incompleteness.