Stability Theorems for the Continuous Spectrum of a Negatively Curved Manifold
- 1 April 1981
- journal article
- Published by JSTOR in Transactions of the American Mathematical Society
- Vol. 264 (2) , 431-448
- https://doi.org/10.2307/1998549
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 ${\Delta _0}$.
Keywords
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