The Essential Spectrum of the Laplacian on Manifolds with Ends
Toshiaki Hattori
Source: Publ. Res. Inst. Math. Sci. Volume 45, Number 2 (2009), 601-644.
Abstract
Let $V$ be a noncompact complete Riemannian manifold. We find a geometric condition which assures that the essential spectrum of the Laplacian on $V$ contains a half-line, by means of fiber bundle structures and the asymptotic behavior of mean curvatures on the ends of $V$, and give lower bounds of the essential spectrum. Our criteria can be applied to locally symmetric spaces of finite volume and manifolds of infinite volume canonically obtained from manifolds with corners.
Primary Subjects: 58J50
Secondary Subjects: 35P15
Full-text: Open access
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Permanent link to this document: http://projecteuclid.org/euclid.prims/1241553131
Digital Object Identifier: doi:10.2977/prims/1241553131
Mathematical Reviews number (MathSciNet):
MR2510513
Zentralblatt MATH identifier:
05591484
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