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Stability theorems for the continuous spectrum of a negatively curved manifold


Author: Harold Donnelly
Journal: Trans. Amer. Math. Soc. 264 (1981), 431-448
MSC: Primary 58G25; Secondary 53C20
DOI: https://doi.org/10.1090/S0002-9947-1981-0603773-0
MathSciNet review: 603773
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Abstract: The spectrum of the Laplacian $ \Delta $ for a simply connected complete negatively curved Riemannian manifold is studied. The Laplacian $ {\Delta _0}$ of a simply connected constant curvature space $ {M_0}$ is known up to unitary equivalence. Decay conditions are given, on the metric $ g$ and curvature $ K$ of $ M$, which imply that the continuous part of $ {\Delta _0}$ is unitarily equivalent to $ {\Delta _0}$.


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DOI: https://doi.org/10.1090/S0002-9947-1981-0603773-0
Article copyright: © Copyright 1981 American Mathematical Society

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