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

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.

References in corpus (3)

• Noncompact complete Riemannian manifolds with dense eigenvalues embedded in the essential spectrum of the Laplacian
• Growth of the eigensolutions of Laplacians on Riemannian manifolds II: positivity of the initial energy
• Growth of the eigensolutions of Laplacians on Riemannian manifolds I: construction of energy function

Cited by in corpus (2)

• Sharp spectral transition for eigenvalues embedded into the spectral bands of perturbed periodic operators
• Growth of the eigensolutions of Laplacians on Riemannian manifolds I: construction of energy function