论文标题
对称表面上的大地测量流
Ergodicity of the geodesic flow on symmetric surfaces
论文作者
论文摘要
我们考虑了Riemann Surface $ x $的Fenchel-Nielsen参数的条件，该参数保证了抛物面类型的表面$ x $。这个问题的一类有趣的Riemann表面是有限的拓扑结尾。在这种情况下，Fenchel-Nielsen坐标的长度部分可以用于{抛物线$ x $}的无穷大。当表面$ x $是对称的终点时，我们证明{$ x $ as parrabolic}等同于第一种覆盖组。然后，我们在半扭对称的表面$ x $的Fenchel-Nielsen坐标上提供了必要的条件，以使{$ x $ is parrabolic}。作为应用程序，我们解决了Basmajian，Hakobyan和第二作者的先前工作中的一个公开问题。
We consider conditions on the Fenchel-Nielsen parameters of a Riemann surface $X$ that guarantee the surface $X$ is of parabolic type. An interesting class of Riemann surfaces for this problem is the one with finitely many topological ends. In this case the length part of the Fenchel-Nielsen coordinates can go to infinity for {parabolic $X$}. When the surface $X$ is end symmetric, we prove that {$X$ being parabolic} is equivalent to the covering group being of the first kind. Then we give necessary and sufficient conditions on the Fenchel-Nielsen coordinates of a half-twist symmetric surface $X$ such that {$X$ is parabolic}. As an application, we solve an open question from the prior work of Basmajian, Hakobyan and the second author.
