论文标题
模量空间中的超密度和有界的大地学
Superdensity and bounded geodesics in moduli space
论文作者
论文摘要
在Beck-Chen之后，我们说，如果有$ c> 0 $，则在公制空间$（x，d）上的流量$ ϕ_t $，如果有$ c> 0 $，则每个$ x \ in x $ in x $ in x $，每个$ t> 0 $，轨迹$ \ \ {ϕ_t x \ \ \} x \ \} _ {0 \ le t \ le t \ le t \ le ct $ ct $ 1/我们表明，如果相关的Teichmüller测量界有界限，则在翻译表面上的线性流是超密集的。相反，如果线性流是超密集的，我们表明沿Teichmüller测量，表面的直径保持界限。这概括了贝克·钦（Beck-chen）在晶格表面上的工作，并让人联想到马苏尔（Masur）在独特的终身制方面的工作。
Following Beck-Chen, we say a flow $ϕ_t$ on a metric space $(X, d)$ is superdense if there is a $c > 0$ such that for every $x \in X$, and every $T>0$, the trajectory $\{ϕ_t x\}_{0 \le t \le cT}$ is $1/T$-dense in $X$. We show that a linear flow on a translation surface is superdense if the associated Teichmüller geodesic is bounded. Conversely, if the linear flow is superdense, we show that along the Teichmüller geodesic, the diameter of the surface remains bounded. This generalizes work of Beck-Chen on lattice surfaces, and is reminiscent of work of Masur on unique ergodicity.
