Symplectic Dynamics Working Group

I will show that a closed, negatively curved Riemannian manifold of 1/4 pinched negative curvature has constant negative curvature if and only if the Lyapunov spectrum of its geodesic flow is the same as that of a hyperbolic manifold. The Lyapunov spectrum describes the asymptotic behavior of vectors under the derivative action of the geodesic flow; the main step of the proof is to convert this asymptotic control into uniform control. I'll also discuss some connections of the techniques used to quasiconformal mapping theory. No background in these topics will be assumed for the talk.