Sufficient conditions in the two-functional conjecture for univalent functions

DOI10.1080/17476933.2013.777712zbMATH Open1305.30013arXiv1210.3996OpenAlexW1999254536WikidataQ122928387 ScholiaQ122928387MaRDI QIDQ5404690

Dmitri Prokhorov

Publication date: 28 March 2014

Published in: Complex Variables and Elliptic Equations (Search for Journal in Brave)

Abstract: The two-functional conjecture says that if a function f analytic and univalent in the unit disk maximizes Re{L} and Re{M} for two continuous linear functionals L and M, L is not equal to cM for any c>0, then f is a rotation of the Koebe function. We use the Loewner differential equation to obtain sufficient conditions in the two-functional conjecture and compare the sufficient conditions with necessary conditions.

Full work available at URL: https://arxiv.org/abs/1210.3996

zbMATH Keywords

Löwner equationtwo-functional conjecture

Mathematics Subject Classification ID

Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.) (30C45) Extremal problems for conformal and quasiconformal mappings, other methods (30C75) Coefficient problems for univalent and multivalent functions of one complex variable (30C50)

Cites Work

• Univalent functions and integrable systems
• A proof of the Bieberbach conjecture
• Coefficients of holomorphic functions
• Quasiconformal variation of slit domains
• On the two-functional conjecture for univalent functions
• The Loewner differential equation and slit mappings

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