Michael Brin (University of Maryland)

On the integrabiblity of the central distribution of a partially hyperbolic diffeomorphism.

Abstract. We show that the central distribution of a partially hyperbolic diffeomorphism $f\colon M\to M$ is uniquely integrable if the stable and unstable foliations are quasi-isometric in the universal cover $\widetilde{M}$, i.e., if the distance in $\widetilde{M}$ between every two points, which lie in the same leaf, is bounded from below by a linear function of the distance along the leaf.