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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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


Authors: Richard Greiner and Oliver Roth
Journal: Proc. Amer. Math. Soc. 129 (2001), 3657-3664
MSC (1991): Primary 30C70, 30C50; Secondary 30C35
Published electronically: May 3, 2001
MathSciNet review: 1860500
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Abstract:

We consider the linear functional $\operatorname{Re} (a_3+ \lambda a_2)$ for $\lambda \in i \mathbb{R}$ on the set of normalized univalent functions in the unit disk and use the result to disprove a conjecture of Bombieri.


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Additional Information

Richard Greiner
Affiliation: Department of Mathematics, Bayerische Julius-Maximilians-Universität, Am Hubland, D-97074 Würzburg, Germany
Email: greiner@mathematik.uni-wuerzburg.de

Oliver Roth
Affiliation: Department of Mathematics, Bayerische Julius-Maximilians-Universität, Am Hubland, D-97074 Würzburg, Germany
Address at time of publication: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109
Email: roth@mathematik.uni-wuerzburg.de

DOI: http://dx.doi.org/10.1090/S0002-9939-01-05994-9
PII: S 0002-9939(01)05994-9
Keywords: Univalent functions, support point, linear functional, fractional linear functional, Schiffer variation
Received by editor(s): December 28, 1999
Received by editor(s) in revised form: May 1, 2000
Published electronically: May 3, 2001
Additional Notes: This paper was completed while the second author was visiting the University of Michigan supported by a Feodor Lynen fellowship of the Alexander von Humboldt foundation. He thanks the faculty and staff for their hospitality.
Communicated by: Albert Baernstein II
Article copyright: © Copyright 2001 American Mathematical Society