On local and global rigidity of uniformly quasiconformal Anosov systems
Abstract. We show that any uniformly quasiconformal contact Anosov flow on a compact manifold of dimension at least 5 is essentially smoothly conjugate to the geodesic flow of a manifold of constant negative curvature. In the discrete time case we show that any transitive uniformly quasiconformal Anosov diffeomorphism, whose stable and unstable distributions have dimensions greater than two, is smoothly conjugate to an Anosov automorphism of a torus. We also describe necessary and sufficient conditions for smoothness of conjugacy between such a diffeomorphism and its C1-small perturbation.