论文标题
平滑的刚性，以实现更高维度接触Anosov流动
Smooth rigidity for higher dimensional contact Anosov flows
论文作者
论文摘要
我们将匹配函数技术应用于触点Anosov流的设置，以满足束假设。这使我们能够概括Feldman-ornstein〜 \ cite {fo}的3维刚性结果。也就是说，我们表明，如果两个这样的Anosov流为$ C^0 $ conjugate，则它们为$ c^{r} $，在[1,2）$中的某些$ r \ in [1,2）$甚至$ c^\ infty $ conjugate conjugate下，根据一些其他假设。例如，这适用于$ 1/4 $ pinched的地球曲面上的紧凑型分节曲率的歧管流动。我们还可以利用结果来恢复Hamendstädt的明显长度频谱刚度结果，以实现真正的双曲线歧管。
We apply the matching functions technique in the setting of contact Anosov flows which satisfy a bunching assumption. This allows us to generalize the 3-dimensional rigidity result of Feldman-Ornstein~\cite{FO}. Namely, we show that if two such Anosov flows are $C^0$ conjugate then they are $C^{r}$, conjugate for some $r\in[1,2)$ or even $C^\infty$ conjugate under some additional assumptions. This, for example, applies to $1/4$-pinched geodesic flows on compact Riemannian manifolds of negative sectional curvature. We can also use our result to recover Hamendstädt's marked length spectrum rigidity result for real hyperbolic manifolds.
