Carathéodory convergence and the conformal type problem

2024/12/08 by Alexandre Erëmenko, Eremenko, Alexandre, Sergei Merenkov +1
Mathematics · #30F99 #Analytic and geometric function theory #Approximation Theory and Sequence Spaces #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.2412.05995

openalex publication_date 2024/12/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study Carathéodory convergence for open, simply connected surfaces spread over the sphere and, in particular, provide examples demonstrating that in the Speiser class the conformal type can change when two singular values collide.

Related

• Convergence of discrete conformal mappings on surfaces
• Asymptotic geometry and conformal types of Carnot--Carathéodory spaces
• Conformally symplectic topology from a dynamical viewpoint
• Singular Yamabe and Obata Problems
• Weak convergence of branched conformal immersions with uniformly bounded areas and Willmore energies