Sullivan sketched a proof of his structural stability theorem for differentiabl group actions satisfying certain expansion-hyperbolicity axioms.

We relax Sullivan’s axioms and introduce a notion of meandering hyperbolicity for group actions on geodesic metric spaces.

This generalization is substantial enough to encompass actions of certain nonhyperbolic groups, such as actions of uniform lattices in semisimple Lie groups on flag manifolds.

At the same time, our notion is sufficiently robust, and we prove that meandering-hyperbolic actions are still structurally stable.

We also prove some basic results on meandering-hyperbolic actions and give other examples of such actions.

This is a joint work with Michael Kapovich and Jaejeong Lee.