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For a class of asymptotically hyperbolic manifolds, we show that the bottomof the continuous spectrum of the Laplace-Beltrami operator is not aneigenvalue. Our approach only uses properties of the operator near infinityand, in particular, does not require any global assumptions on the topology orthe curvature, unlike previous papers on the same topic.

Absence of eigenvalue at the bottom of the continuous spectrum on asymptotically hyperbolic manifolds