Carathéodory convergence and the conformal type problem

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This is a Quantitative Study study.

Alexandre Erëmenko; Sergei Merenkov

doi:10.54330/afm.176092

October 6, 2025Annales Fennici MathematiciOpen Access

Carathéodory convergence and the conformal type problem

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Key Points

Carathédory convergence identifies shifts in conformal type within the Speiser class.
The study illustrates that singular values can collide, altering conformal characteristics significantly.
Open and simply connected surfaces spread over the sphere show notable geometric transformations.
Interconnections between Carathédory convergence and surface properties reveal complex behaviors.

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Implication

Analysis uncovers changes in conformal type linked to singular value collisions in open surfaces, implying deeper geometric insights.

Abstract

We study Carathédory 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.

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Cite This Study

Erëmenko et al. (2025) studied this question.

synapsesocial.com/papers/68e5c1c76950a706b22b5e1d https://doi.org/10.54330/afm.176092

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Carathéodory convergence and the conformal type problem

Key Points

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Implication

Abstract

Discussion

Cite This Study

Carathéodory convergence and the conformal type problem

Key Points

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Implication

Abstract

Discussion

Cite This Study

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