Hyperbolic triangles without embedded eigenvalues
Spectral Theory
2017-11-07 v2 Classical Analysis and ODEs
Differential Geometry
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.
Cite
@article{arxiv.1402.4533,
title = {Hyperbolic triangles without embedded eigenvalues},
author = {Luc Hillairet and Chris Judge},
journal= {arXiv preprint arXiv:1402.4533},
year = {2017}
}
Comments
65 pages, 4 figures, to appear in Annals of Mathematics http://annals.math.princeton.edu/articles/11599