标题： 三维四分之一夹紧负曲率流形的框架流的指数混合 显示英文标题

标题： Exponential mixing of frame flows for three dimensional manifolds of quarter-pinched negative curvature

摘要： 对于具有严格1/4夹紧负截面曲率的紧致三维光滑黎曼流形，我们建立了框架流相对于归一化体积的指数混合性。 更一般地，这个结果扩展到Anosov流的一类环面扩张，前提是关于Brin传递群和稳定子丛的光滑性有假设条件。 我们的方法基于通过底层Anosov流的Young塔构建的一个简化的动力学模型来研究扩展流。 然后通过对应转移算子的加强型Dolgopyat类型估计获得指数混合性。 显示英文摘要

摘要： 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.