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

2025/07/22 by Yan Mary He, He, Yan Mary, Ho-Min Lee +3
Chemical Engineering · Materials Science · #32G15 #37F10 #37F30 #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT) #Polymer Foaming and Composites #Rheology and Fluid Dynamics Studies

paper · pdf · doi:10.48550/arxiv.2507.17077

openalex publication_date 2025/07/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study complex analytic aspects of the moduli space \Bcal_d^fm of degree d≥2 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 SA^fm_d, which is a codimension-1 subspace of \Bcal^fm_d.

Citations

• Pressure path metrics on parabolic families of polynomials
• On geometrically finite degenerations II: convergence and divergence
• On geometrically finite degenerations I: boundaries of main hyperbolic components
• The geometry of the Weil-Petersson metric in complex dynamics
• Hyperbolic Components

Related

• Pressure metrics in geometry and dynamics
• Maximal Blaschke Products
• On critical points of Blaschke products
• A note on connectedness of Blaschke products
• A note on the characterization of finite Blaschke products