Schlicht regions for entire and meromorphic functions
type: Item
instance of: scholarly article
title: Schlicht regions for entire and meromorphic functions
zbMATH Open document ID: 0924.30039
DOI: 10.1007/BF02791258
published in: Journal d'Analyse Mathématique
publication date: 1999-11-07T00:00:00Z
review text: Let \(X\) be a Riemann surface, \(f:X\to\overline{\mathbb C}\) be a meromorphic function, \(M\) be some class of meromorphic functions on \(X\). Let \(p\in X\) and \(d_f(p)\) be the radius of the largest spherical disc centered at \(f(p)\) in which the function \(f^{-1}\) is holomorphic. The Bloch constants are defined as follows: \[ B_f=\sup_{p\in X}d_f(p),\qquad B(X,M)=\inf_{f\in M}B_f . \] The evaluation of \(B(X,M)\) when \(X={\mathbb C}\), \(M\) being the class of all meromorphic functions is an open problem. The authors prove that \(B({\mathbb C},E)=\frac\pi{2}\) where \(E\) is the class of all entire functions. They investigate other cases as well.
Mathematics Subject Classification ID: 30D45
zbMATH DE Number: 1309901
zbMATH Keywords: Bloch constants
zbMATH Keywords: normal family
zbMATH Keywords: Riemann surface
zbMATH Keywords: spherical geometry
author: Mario Bonk
author: Alexandre Eremenko
MaRDI profile type: Publication
Wikidata QID: Q125291014
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description: scientific article; zbMATH DE number 1309901