Concentration of area in half-planes

Roger W. Barnard; Clint Richardson; Alexander Yu Solynin

doi:10.1090/S0002-9939-05-07775-0

Concentration of area in half-planes

Roger W. Barnard, Clint Richardson, Alexander Yu Solynin

Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

Abstract

For the standard class S of normalized univalent functions f analytic in the unit disk U, we consider a problem on the minimal area of the image f(U) concentrated in any given half-plane. This question is related to a well-known problem posed by A. W. Goodman in 1949 that regards minimizing area covered by analytic univalent functions under certain geometric constraints. An interesting aspect of this problem is the unexpected behavior of the candidates for extremal functions constructed via geometric considerations.

Original language	English
Pages (from-to)	2091-2099
Number of pages	9
Journal	Proceedings of the American Mathematical Society
Volume	133
Issue number	7
DOIs	https://doi.org/10.1090/S0002-9939-05-07775-0
State	Published - Jul 2005

Keywords

Local variation
Minimal area problem
Symmetrization
Univalent function

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10.1090/S0002-9939-05-07775-0

Cite this

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KW - Local variation

KW - Minimal area problem

KW - Symmetrization

KW - Univalent function

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Concentration of area in half-planes

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Keywords

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