Limits of limit sets in rank-one symmetric spaces - Archive ouverte HAL
Pré-Publication, Document De Travail Année : 2024

Limits of limit sets in rank-one symmetric spaces

Résumé

We consider the question of continuity of limit sets for sequences of geometrically finite subgroups of isometry groups of rank-one symmetric spaces, and prove analogues of classical (Kleinian) theorems in this context. In particular we show that, assuming strong convergence of the sequence of subgroups, the limit sets vary continuously with respect to Hausdorff distance, and if the sequence is weakly type-preserving, the sequence of Cannon-Thurston maps also converges uniformly to a limiting Cannon-Thurston map. Our approach uses the theory of extended geometrically finite representations, developed recently by the second author.

Dates et versions

hal-04659677 , version 1 (23-07-2024)

Licence

Identifiants

Citer

Antonin Guilloux, Theodore Weisman. Limits of limit sets in rank-one symmetric spaces. 2024. ⟨hal-04659677⟩
21 Consultations
0 Téléchargements

Altmetric

Partager

More