Boundaries of acylindrically hyperbolic groups and applications

• Applicant: Professorin Dr. Ursula Hamenstädt
• Subject Area: Mathematics
• Term: from 2017 to 2023
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 338192326

The project is devoted to the Investigation of topological and geometric properties of finitely generated groups which admit an acylindrical action on some hyperbolic space, in particular regarding their asymptotic geometry. The main distant goal is the construction of universally amenable compact boundaries as well as of affine isometric actions on L^p-spaces. Furthermore we aim at establishing rigidity properties for asymptotical invariants of fundamental groups of closed negatively curved manifolds.

• DFG Programme: Priority Programmes
• Subproject of: SPP 2026: Geometry at Infinity