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- Publisher
- Wiley
- Copyright
- © 2021 London Mathematical Society
- ISSN
- 0024-6093
- eISSN
- 1469-2120
- DOI
- 10.1112/blms.12501
- Publisher site
- See Article on Publisher Site
Abstract
We construct a surface with a cylindrical end which has a finite number of Laplace eigenvalues embedded in its continuous spectrum. The surface is obtained by attaching a cylindrical end to a hyperbolic torus with a hole. To our knowledge, this is the first example of a manifold with a cylindrical end whose number of eigenvalues is known to be finite and nonzero. The construction can be varied to give examples with arbitrary genus and with an arbitrarily large finite number of eigenvalues. The constructed surfaces also have resonance‐free regions near the continuous spectrum and long‐time asymptotic expansions of solutions to the wave equation.
Journal
Bulletin of the London Mathematical Society – Wiley
Published: Oct 1, 2021
Keywords: 58J50 (primary)