Stability theorems for the continuous spectrum of a negatively curved manifold
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- by Harold Donnelly
- Trans. Amer. Math. Soc. 264 (1981), 431-448
- DOI: https://doi.org/10.1090/S0002-9947-1981-0603773-0
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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 ${\Delta _0}$.References
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Bibliographic Information
- © Copyright 1981 American Mathematical Society
- 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