Hyperbolic triangles without embedded eigenvalues - Archive ouverte HAL Access content directly
Journal Articles Annals of Mathematics Year : 2018

Hyperbolic triangles without embedded eigenvalues

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.
Fichier principal
Vignette du fichier
1402.4533.pdf (1.09 Mo) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-01081346 , version 1 (31-03-2015)

Identifiers

Cite

Luc Hillairet, Chris Judge. Hyperbolic triangles without embedded eigenvalues. Annals of Mathematics, 2018, 187 (2), pp.301-377. ⟨10.4007/annals.2018.187.2.1⟩. ⟨hal-01081346⟩
124 View
70 Download

Altmetric

Share

Gmail Facebook X LinkedIn More