English

Noncompact complete Riemannian manifolds with dense eigenvalues embedded in the essential spectrum of the Laplacian

Differential Geometry 2019-04-10 v2 Mathematical Physics math.MP Spectral Theory

Abstract

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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Cite

@article{arxiv.1805.01072,
  title  = {Noncompact complete Riemannian manifolds with dense eigenvalues embedded in the essential spectrum of the Laplacian},
  author = {Svetlana Jitomirskaya and Wencai Liu},
  journal= {arXiv preprint arXiv:1805.01072},
  year   = {2019}
}

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