Exponential Mixing of Frame Flow for Convex Cocompact Hyperbolic Manifolds

The aim of this paper is to establish exponential mixing of frame flow for the measure of maximal entropy on a convex cocompact hyperbolic manifold. Consequences include results on the decay of matrix coefficients and on effective equidistribution of holonomies. The main technical point is a spectral bound on certain twisted transfer operators, which we obtain by building on Dolgopyat’s framework. This extends and strengthens earlier work of Dolgopyat, Stoyanov, Pollicott, and others.