论文标题
无限riemann表面上的二次差异和叶子
Quadratic differentials and foliations on infinite Riemann surfaces
论文作者
论文摘要
我们证明，无限的Riemann Surface $ x $是抛物线（$ x \ in O_g $），并且仅当任何可跨切割的任何可整合全体形态二次差异的水平轨迹的结合为零。然后，当在O_G $中$ x \时，我们在所有可集成的二次差异空间中建立了Jenkins-Strebel差异的密度，并在这种情况下扩展了Kerckhoff的TeichMüller指标的公式。我们的方法取决于扩展到无限表面的Hubbard-Masur定理，描述了哪些测得的叶子可以通过可集成的全体形态二次差异的水平轨迹来实现。
We prove that an infinite Riemann surface $X$ is parabolic ($X\in O_G$) if and only if the union of the horizontal trajectories of any integrable holomorphic quadratic differential that are cross-cuts is of zero measure. Then we establish the density of the Jenkins-Strebel differentials in the space of all integrable quadratic differentials when $X\in O_G$ and extend Kerckhoff's formula for the Teichmüller metric in this case. Our methods depend on extending to infinite surfaces the Hubbard-Masur theorem describing which measured foliations can be realized by horizontal trajectories of integrable holomorphic quadratic differentials.
