Hyperbolic triangles without embedded eigenvalues

Luc Hillairet; Chris Judge

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arXiv · 1402.4533

Hyperbolic triangles without embedded eigenvalues

Luc Hillairet·Chris Judge

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Abstract

We consider the Neumann Laplacian acting on square-integrable functions on a triangle in the hyperbolic plane that has one cusp. We show that the generic such triangle has no eigenvalues embedded in its continuous spectrum. To prove this result we study the behavior of the real-analytic eigenvalue branches of a degenerating family of triangles. In particular, we use a careful analysis of spectral projections near the crossings of these eigenvalue branches with the eigenvalue branches of a model operator.

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BibTeX RIS

Luc Hillairet, Chris Judge. 2014-02-19. Hyperbolic triangles without embedded eigenvalues. https://arxiv.org/abs/1402.4533

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