The research demonstrates simultaneous uniformization and analyzes pressure semi-norms in Blaschke products.
In this paper, we study complex analytic aspects of the moduli space dᶠᵐ of degree d≥2 fixed-point-marked Blaschke products. We define a complex structure on dᶠᵐ and prove the simultaneous uniformization theorem for fixed-point-marked quasi-Blaschke products. As an application, we show that the pressure semi-norms on the space of Blaschke products are non-degenerate outside of the super-attracting locus SAᶠᵐd, which is a codimension-1 subspace of ᶠᵐd.
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He et al. (2025) studied this question.
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