This research establishes that the intersection number remains finite for horizontal foliations of quadratic differentials, highlighting continuity in the L¹ norm.
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 L¹-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.
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Šarić et al. (2025) studied this question.
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