论文标题
大地电流的长度比较定理
A length comparison theorem for geodesic currents
论文作者
论文摘要
我们与封闭的Euler特征的封闭表面$ s $ s $ \ mathcal c（s）$合作。在作者对Sebastian Hensel作者的先前工作，每个填充地球当前$μ$在TeichmüllerSpace中具有独特的长度最小化度量$ x $。在本文中，我们表明，在所谓的$ x $的厚组件上，$μ$和$ x $的几何形状是可比性的，最多可达标量，具体仅取决于$μ$和$ s $的拓扑。我们还仅使用$μ$的长度函数来表征投影的厚组件。
We work with the space $\mathcal C(S)$ of geodesic currents on a closed surface $S$ of negative Euler characteristic. By prior work of the author with Sebastian Hensel, each filling geodesic current $μ$ has a unique length-minimizing metric $X$ in Teichmüller space. In this paper, we show that, on so-called thick components of $X$, the geometries of $μ$ and $X$ are comparable, up to a scalar depending only on $μ$ and the topology of $S$. We also characterize thick components of the projection using only the length function of $μ$.
