Equicontinuity by the prime ends of mappings with the normalization condition

2020/04/09 by Evgeny Sevost’yanov, Sevost'yanov, E. A., Nataliya Ilkevych +1
Mathematics · #30C65 #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.2004.04801

openalex publication_date 2020/04/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study branching mappings that satisfy some condition of distortion of the modulus of families of paths. In a situation where the definition domain of mappings is locally connected on its boundary, the mapped domain is regular, and the majorant responsible for distortion of the modulus of families of paths is integrable, it is proved that the families of all specified mappings with one normalization condition are equicontinuous in the closure of the given domain.

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