This article is cited in 6 papers

A discreteness criterion for the spectrum of the Laplace–Beltrami operator on quasimodel manifolds

A. V. Svetlov

Volgograd State University

Abstract: We study the spectrum of the Laplace–Beltrami operator on noncompact Riemannian manifolds of a special form, in particular on model manifolds. We obtain a discreteness criterion for the spectrum in terms of the volume and capacity of some domains on a manifold.

Keywords: noncompact Riemannian manifold, Laplace–Beltrami operator, discrete spectrum.

UDC: 517.95

Received: 16.01.2002

 English version: Siberian Mathematical Journal, 2002, 43:6, 1103–1111

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