Exponential mixing of frame flows for three dimensional manifolds of quarter-pinched negative curvature
Abstract
For a compact three-dimensional smooth Riemannian manifold of strictly 1/4-pinched negative sectional curvature, we establish exponential mixing of the frame flow with respect to the normalized volume. More generally this result extends to a class of torus extensions of Anosov flows, subject to assumptions on the Brin transitivity group and the smoothness of the stable subbundle. Our approach is based on a simplified dynamical model for studying the extension flow, constructed via a Young tower of the underlying Anosov flow. Exponential mixing is then obtained through a strengthened Dolgopyat type estimate on the corresponding transfer operators.
Keywords
Cite
@article{arxiv.2508.01593,
title = {Exponential mixing of frame flows for three dimensional manifolds of quarter-pinched negative curvature},
author = {Daofei Zhang},
journal= {arXiv preprint arXiv:2508.01593},
year = {2025}
}
Comments
A miscalculation led to the invalidation of the previous discussion that bypassed the regularity of the stable foliation of the frame flow is not C1.Thus, the main result on 3-D frame flows is not effective