Exponential mixing of frame flows for convex cocompact hyperbolic manifolds

Abstract

The aim of this paper is to establish exponential mixing of frame flows for convex cocompact hyperbolic manifolds of arbitrary dimension with respect to the Bowen-Margulis-Sullivan measure. Some immediate applications include an asymptotic formula for matrix coefficients with an exponential error term as well as the exponential equidistribution of holonomy of closed geodesics. The main technical result is a spectral bound on transfer operators twisted by holonomy, which we obtain by building on Dolgopyat's method.

55 pages, 2 figures; minor improvements added to the first version during publication

Cited by in corpus (5)

• Exponential mixing of frame flows for geometrically finite hyperbolic manifolds
• Exponential mixing of geodesic flows for geometrically finite hyperbolic manifolds with cusps
• Generalization of Selberg's $3/16$ theorem for convex cocompact thin subgroups of $\mathrm{SO}(n,1)$
• Spectral theory of the frame flow on hyperbolic 3-manifolds (with an appendix by Charles Hadfield)
• The fractal uncertainty principle via Dolgopyat's method in higher dimensions