Covering theorems for meromorphic functions
type: Item
instance of: scholarly article
title: Covering theorems for meromorphic functions
zbMATH Open document ID: 0568.30042
DOI: 10.1007/BF02790199
author: U Srebro
published in: Journal d'Analyse Mathématique
publication date: 1985-01-01T00:00:00Z
review text: Let f be a meromorphic function in a domain \({\mathcal D}\subset {\bar {\mathbb{C}}}\). Denote by n(w) the number card \(f^{-1}(w)\), \(w\in {\bar {\mathbb{C}}}\) (counting multiplicities). The function f is p-valent if \(\max_{w}n(w)=p\). The author studies some topological properties of p- valent functions. For example: If f is p-valent in the unit disk then the set \(\{\) w: n(w)\(\leq p-1\}\) contains a non-degenerate continuum. If in addition the total branch order \(\neq 2p-2\) then \(n(w_ 0)\leq p-2\) for at least one point \(w_ 0\in {\bar {\mathbb{C}}}\).
Mathematics Subject Classification ID: 30G12
Mathematics Subject Classification ID: 30C55
zbMATH DE Number: 3906842
zbMATH Keywords: ramified coverings
zbMATH Keywords: open functions
zbMATH Keywords: cluster sets
zbMATH Keywords: p-valent functions
reviewed by: Alexandre Eremenko
MaRDI profile type: Publication
cites work: Some Covering Theorems for Analytic Functions
cites work: Q5527882
cites work: Q3931656
cites work: A Covering Surface Conjecture of Brannan and Kirwan
cites work: On the local behavior of quasiregular maps and branched covering maps
cites work: Deficiences of immersions
cites work: Q5580899
description: scientific article; zbMATH DE number 3906842