Critical exponent and bottom of the spectrum in pinched negative curvature

Abstract : In this note, we present a new proof of the celebrated theorem of Patterson–Sullivan which relates the critical exponent of a hyperbolic manifold and the bottom of its spectrum. The proof extends to manifolds with pinched negative curvatures. It provides a sufficient criterion for the existence of isolated eigenvalues for the Laplacian on geometrically finite manifolds with pinched negative curvatures.
Type de document :
Article dans une revue
Mathematical Research Letters, 2015, 22 (3), pp.929 - 944. 〈10.4310/MRL.2015.v22.n3.a15〉
Liste complète des métadonnées

https://hal.archives-ouvertes.fr/hal-01729692
Contributeur : Samuel Tapie <>
Soumis le : lundi 12 mars 2018 - 17:15:05
Dernière modification le : vendredi 4 janvier 2019 - 17:32:34

Identifiants

Citation

Thomas Roblin, Samuel Tapie. Critical exponent and bottom of the spectrum in pinched negative curvature. Mathematical Research Letters, 2015, 22 (3), pp.929 - 944. 〈10.4310/MRL.2015.v22.n3.a15〉. 〈hal-01729692〉

Partager

Métriques

Consultations de la notice

192