On support points of univalent functions and a disproof of a conjecture of Bombieri

DOI10.1090/S0002-9939-01-05994-9zbMath0981.30018WikidataQ122924220 ScholiaQ122924220MaRDI QIDQ2750863

Oliver Roth, Richard Greiner

Publication date: 21 October 2001

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

linear functionalunivalent functionssupport pointSchiffer variationfractional linear functional

Mathematics Subject Classification ID

General theory of conformal mappings (30C35) Extremal problems for conformal and quasiconformal mappings, variational methods (30C70) Coefficient problems for univalent and multivalent functions of one complex variable (30C50)

Related Items (10)

Analogy of Bombieri's number for bounded univalent functions ⋮ Value Regions in Classes of Conformal Mappings ⋮ Harmonic Measures of Slit Sides, Conformal Welding and Extremum Problems ⋮ A problem of Bombieri on univalent functions ⋮ On the Bombieri numbers for the class S ⋮ Necessary criteria for the Bombieri conjecture ⋮ On the failure of Bombieri's conjecture for univalent functions ⋮ Qualitative results in the Bombieri problem for conformal mappings ⋮ The Bombieri problem for bounded univalent functions ⋮ Classical and Stochastic Löwner–Kufarev Equations

Cites Work

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• Univalent functions maximizing Re{a//3+lambdaa//2}
• Extremum problems for bounded univalent functions II
• On the local maximum property of the Koebe function
• On the extreme points of classes of univalent functions
• Topics in Complex Analysis
• A Variation of the Koebe Mapping in a Dense Subset of S
• On the Functional in the ClassS
• Non-homogeneous combinations of coefficients of univalent functions

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