论文标题
平滑的刚性，以保留Anosov流动和加权标记长度刚度的3维体积
Smooth rigidity for 3-dimensional volume preserving Anosov flows and weighted marked length spectrum rigidity
论文作者
论文摘要
令$ x_1^t $和$ x_2^t $ Be BE量化保存Anosov在3维歧管$ M $上流动。我们证明，如果$ x_1^t $和$ x_2^t $是$ c^0 $ conjugate，则实际上，除非$ m $是$ \ mathbb t^2 $的Anosov自动形态的映射曲线，否则结合性是平稳的，并且两个流都是恒定的屋顶悬架流。我们推断出多个应用程序。其中是对$ \ mathbb t^2 $的Anosov差异性的刚性的新结果，以及负曲率表面的新“加权”明显的长度频谱刚度结果。
Let $X_1^t$ and $X_2^t$ be volume preserving Anosov flows on a 3-dimensional manifold $M$. We prove that if $X_1^t$ and $X_2^t$ are $C^0$ conjugate then the conjugacy is, in fact, smooth, unless $M$ is a mapping torus of an Anosov automorphism of $\mathbb T^2$ and both flows are constant roof suspension flows. We deduce several applications. Among them is a new result on rigidity of Anosov diffeorphisms on $\mathbb T^2$ and a new "weighted" marked length spectrum rigidity result for surfaces of negative curvature.
