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arXiv · 2510.21365

Volume of unit balls associated to quadratic differentials

Weixu Su·Shenxing Zhang
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Abstract

Associated to a holomorphic quadratic differential is a unit ball of the measured lamination space. The Thurston volume of the unit ball defines a function on the moduli space. We show that the volume function is not proper and characterize when it tends to infinity. We prove that the volume function is $p$-integrable for any $0<p<1$.

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Weixu Su, Shenxing Zhang. 2025-10-24. Volume of unit balls associated to quadratic differentials. https://arxiv.org/abs/2510.21365

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