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arXiv · 2507.17077

Analytic Theory on the Space of Blaschke Products: Simultaneous Uniformization and Weil-Petersson Metric

Yan Mary He·Homin Lee·Insung Park
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Abstract

In this paper, we study complex analytic aspects of the moduli space $\Bcal_d^{fm}$ of degree $d\ge2$ fixed-point-marked Blaschke products. We define a complex structure on $\Bcal_d^{fm}$ and prove the simultaneous uniformization theorem for fixed-point-marked quasi-Blaschke products. As an application, we show that the Weil-Petersson semi-norm (which is also referred to as the pressure semi-norm) is non-degenerate along all directions transverse to a holomorphic codimension-1 foliation of $\Bcal^{fm}_d$.

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Yan Mary He, Homin Lee, Insung Park. 2026-09-15. Analytic Theory on the Space of Blaschke Products: Simultaneous Uniformization and Weil-Petersson Metric. https://arxiv.org/abs/2507.17077

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