Noncompact complete Riemannian manifolds with dense eigenvalues embedded in the essential spectrum of the Laplacian
We prove sharp criteria on the behavior of radial curvature for the existence of asymptotically flat or hyperbolic Riemannian manifolds with prescribed sets of eigenvalues embedded in the spectrum of the Laplacian. In particular, we construct such manifolds with dense embedded point spectrum and sharp curvature bounds.
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We are grateful to A. Mramor for sharing with us the review [Don10], which led to the idea of this project. W.L. would like to thank M. Lukic and H. Xu for some useful discussions. W.L. was supported by the AMS-Simons Travel Grant 2016-2018. This research was supported by NSF DMS-1401204 and NSF DMS-1700314.
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