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

  • Svetlana JitomirskayaEmail author
  • Wencai Liu
Article

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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Notes

Acknowledgments

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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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of CaliforniaIrvineUSA

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