标题： 二次微分水平叶状结构之间的交点数 显示英文标题

标题： Intersection numbers between horizontal foliations of quadratic differentials

摘要： 我们证明了任意两个定义在任意黎曼曲面上的有限面积全纯二次微分的水平叶理之间的相交数是有限的。 我们的主要结果表明，该相交数在二次微分的$L^1$-范数下是联合连续的。 由此得出的一个推论是，当无穷黎曼曲面不是抛物面时，詹金斯-斯特雷贝尔微分在所有有限面积全纯二次微分的空间中并不稠密。 显示英文摘要

摘要： We establish that the intersection number between the horizontal foliations of any two finite-area holomorphic quadratic differentials on an arbitrary Riemann surface is finite. Our main result shows that the intersection number is jointly continuous in the $L^1$-norm on the quadratic differentials. A corollary is that the Jenkins-Strebel differentials are not dense in the space of all finite-area holomorphic quadratic differentials when the infinite Riemann surface is not parabolic.