Hyperbolic triangles without embedded eigenvalues - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Annals of Mathematics Année : 2018

Hyperbolic triangles without embedded eigenvalues

Résumé

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
Origine Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

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

Identifiants

Citer

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⟩
126 Consultations
70 Téléchargements

Altmetric

Partager

Gmail Mastodon Facebook X LinkedIn More