Discreteness of the spectrum of the Laplace-Beltrami operator

Details Discreteness of the spectrum of the Laplace-Beltrami operator Discreteness of the spectrum of the Laplace-Beltrami operator

2007-01-20

arxiv.org/abs/math/0701564v1

Journal of Geometric Analysis, 19 (2009), 358--372

Mathematics

Functional Analysis

Scientific paper

10.1007/s12220-008-9055-6

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.

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