标题： 解析理论在Blaschke乘积空间上：同时一致化和压强度量 显示英文标题

标题： Analytic Theory on the Space of Blaschke Products: Simultaneous Uniformization and Pressure Metric

摘要： 在本文中，我们研究了次数为$d\ge2$的固定点标记 Blaschke 乘积的模空间$\Bcal_d^{fm}$的复解析方面。我们定义了$\Bcal_d^{fm}$上的复结构，并证明了固定点标记准 Blaschke 乘积的同时统一化定理。作为应用，我们表明 Blaschke 乘积空间上的压力半范数在超吸引局部以外是非退化的$\mathcal{SA}^{fm}_d$，这是$\Bcal^{fm}_d$中的一个余维-1 子空间。 显示英文摘要

摘要： 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 pressure semi-norms on the space of Blaschke products are non-degenerate outside of the super-attracting locus $\mathcal{SA}^{fm}_d$, which is a codimension-1 subspace of $\Bcal^{fm}_d$.