论文标题
垂出双曲线表面和密度特性的电流
Currents on cusped hyperbolic surfaces and denseness property
论文作者
论文摘要
在双曲表面$σ$上的太空$ \ mathrm {gc}（σ）$可以被视为完成$σ$紧凑的一套加权封闭的大地质量的完成，因为$σ$紧凑，因为一组对相对应的$σ$的合理地理ecodesic cournent $ \ mathrm {gc}（σ）$。我们证明，即使$σ$是具有有限区域的双曲线表面，$ \ mathrm {gc}（σ）$也具有理性的地理电流的密度属性，不仅与$σ$的加权封闭的大地测量相对应，还与连接两个cusps连接的加权地理位置相对应。此外，我们提出了一个示例，其中一系列加权封闭的大地测量学序列会收敛到连接两个尖端的大地测量，这是交叉数字连续扩展至$ \ mathrm {gc}（σ）$的障碍物。为了构建示例，我们使用子集电流的概念。最后，我们证明了cus的双曲线表面上的子集电流的空间具有有理子集电流的密度特性。
The space $\mathrm{GC} (Σ)$ of geodesic currents on a hyperbolic surface $Σ$ can be considered as a completion of the set of weighted closed geodesics on $Σ$ when $Σ$ is compact, since the set of rational geodesic currents on $Σ$, which correspond to weighted closed geodesics, is a dense subset of $\mathrm{GC}(Σ)$. We prove that even when $Σ$ is a cusped hyperbolic surface with finite area, $\mathrm{GC}(Σ)$ has the denseness property of rational geodesic currents, which correspond not only to weighted closed geodesics on $Σ$ but also to weighted geodesics connecting two cusps. In addition, we present an example in which a sequence of weighted closed geodesics converges to a geodesic connecting two cusps, which is an obstruction for the intersection number to extend continuously to $\mathrm{GC}(Σ)$. To construct the example, we use the notion of subset currents. Finally, we prove that the space of subset currents on a cusped hyperbolic surface has the denseness property of rational subset currents.
