Noncompact complete Riemannian manifolds with singular continuous spectrum embedded into the essential spectrum of the Laplacian, I. The hyperbolic case

Jitomirskaya, Svetlana; Liu, Wencai

doi:10.1090/tran/8112

Noncompact complete Riemannian manifolds with singular continuous spectrum embedded into the essential spectrum of the Laplacian, I. The hyperbolic case
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Abstract:

We construct Riemannian manifolds with singular continuous spectrum embedded in the absolutely continuous spectrum of the Laplacian. Our manifolds are asymptotically hyperbolic with sharp curvature bounds.

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