Carath\'eodory convergence and the conformal type problem

TL;DR

This paper investigates how Carathéodory convergence affects the conformal type of simply connected surfaces, showing that in the Speiser class, the conformal type can change when singular values collide.

Contribution

It provides new examples demonstrating the change in conformal type during Carathéodory convergence in the Speiser class.

Findings

Conformal type can change due to singular value collision.

Carathéodory convergence impacts the conformal structure of surfaces.

Examples illustrating the phenomenon in the Speiser class.

Abstract

We study Carath\'eodory 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.