On a theorem of Baernstein
type: Item
instance of: scholarly article
title: On a theorem of Baernstein
zbMATH Open document ID: 0831.30004
DOI: 10.1007/BF02559610
author: Enrique Villamor
published in: Arkiv för Matematik
publication date: 1996-02-12T00:00:00Z
review text: \textit{A. Baernstein II} (J. Anal. Math. 53, 253-268 (1989; Zbl 0689.30017) considered the following problem. Let \(\Theta\) be the complement on the sphere of the continuum consisting of the union of the ray on the real axis from \(- \infty\) to 1 and the segment from 0 to \(a = \exp i \pi/3\). Let \(F_1 (z)\), \(F_2 (y)\) map \(\Theta\) onto the plane slit along the negative real axis such that \(F_1 (1) = 0\), \(F_2 (a) = 0\), \(\lim_{z \to \infty} |F_i (z)/z |= 1\), \(i = 1,2\). Let \(y = \lim_{z \to 1} |{F_1 (z) \over z - 1} |\); \(\beta = \lim_{z \to a} |{F_2 (z) \over z - a} |\). He asserts that \(y^{1/2} + \beta^{1/2} > \sqrt 2\). Baernstein's presentation depends on complicated estimates and numerical calculations. The present author gives a conceptual proof using the method of the extremal metric and techniques introduced by \textit{K. Oikawa} and the reviewer [Ill. J. Math. 15, 664-671 (1971; Zbl 0229.30012)].
reviewed by: James A. Jenkins
Mathematics Subject Classification ID: 30C20
Mathematics Subject Classification ID: 31A15
zbMATH DE Number: 792860
MaRDI profile type: Publication
cites work: A counterexample concerning integrability of derivatives of conformal mappings
cites work: Quasilines and conformal mappings
cites work: Q3328781
cites work: Level sets of univalent functions
cites work: On results of Ahlfors and Hayman
cites work: Numerical Computation of the Schwarz–Christoffel Transformation
Recommended article: On a Theorem Of Baer and Higman
Recommended article: A note on a theorem of Baer
Recommended article: On a theorem of Bernstein
Recommended article: On Baer's theorem and its generalizations
Recommended article: On a theorem of Behrend
Recommended article: On a theorem of Berkovich
Recommended article: A remark on a theorem of Baer
Recommended article: Q5843335
Recommended article: On a theorem of Baumgartner and Weese
Recommended article: ON A THEOREM OF BESICOVITCH
description: scientific article; zbMATH DE number 792860