On the essential spectrum of the Laplacian on complete manifolds
نویسندگان
چکیده
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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 m...
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In this paper, we prove that the Lp essential spectra of the Laplacian on functions are [0,+∞) on a noncompact complete Riemannian manifold with non-negative Ricci curvature at infinity. The similar method applies to gradient shrinking Ricci soliton, which is similar to non-compact manifold with non-negative Ricci curvature in many ways. © 2010 Elsevier Inc. All rights reserved.
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ژورنال
عنوان ژورنال: Journal of the Mathematical Society of Japan
سال: 1997
ISSN: 0025-5645
DOI: 10.2969/jmsj/04910001