A minimal area problem in conformal mapping

Dov Aharonov; Harold S. Shapiro; Alexander Yu Solynin

doi:10.1007/BF02791132

A minimal area problem in conformal mapping

Dov Aharonov, Harold S. Shapiro, Alexander Yu Solynin

Mathematics and Statistics

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Abstract

Let S denote the usual class of functions f holomorphic and univalent in the unit disk U such that f(0) = f′(0) - 1 = 0. The main result of the paper is that area(f(U)) ≥ (27π/8)(2 - α)^-2 for all f ∈ S such that |f″(0)| = 2α, 1/2 < α < 2. This solves a long-standing extremal problem for the class of functions considered.

Original language	English
Pages (from-to)	157-176
Number of pages	20
Journal	Journal d'Analyse Mathematique
Volume	78
DOIs	https://doi.org/10.1007/BF02791132
State	Published - 1999

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@article{e690085e8b4c48fe9b469a78971c1da1,

title = "A minimal area problem in conformal mapping",

abstract = "Let S denote the usual class of functions f holomorphic and univalent in the unit disk U such that f(0) = f′(0) - 1 = 0. The main result of the paper is that area(f(U)) ≥ (27π/8)(2 - α)-2 for all f ∈ S such that |f″(0)| = 2α, 1/2 < α < 2. This solves a long-standing extremal problem for the class of functions considered.",

author = "Dov Aharonov and Shapiro, {Harold S.} and Solynin, {Alexander Yu}",

year = "1999",

doi = "10.1007/BF02791132",

language = "English",

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pages = "157--176",

journal = "Journal d'Analyse Mathematique",

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TY - JOUR

T1 - A minimal area problem in conformal mapping

AU - Aharonov, Dov

AU - Shapiro, Harold S.

AU - Solynin, Alexander Yu

PY - 1999

Y1 - 1999

N2 - Let S denote the usual class of functions f holomorphic and univalent in the unit disk U such that f(0) = f′(0) - 1 = 0. The main result of the paper is that area(f(U)) ≥ (27π/8)(2 - α)-2 for all f ∈ S such that |f″(0)| = 2α, 1/2 < α < 2. This solves a long-standing extremal problem for the class of functions considered.

AB - Let S denote the usual class of functions f holomorphic and univalent in the unit disk U such that f(0) = f′(0) - 1 = 0. The main result of the paper is that area(f(U)) ≥ (27π/8)(2 - α)-2 for all f ∈ S such that |f″(0)| = 2α, 1/2 < α < 2. This solves a long-standing extremal problem for the class of functions considered.

UR - http://www.scopus.com/inward/record.url?scp=0012094532&partnerID=8YFLogxK

U2 - 10.1007/BF02791132

DO - 10.1007/BF02791132

M3 - Article

AN - SCOPUS:0012094532

SN - 0021-7670

VL - 78

SP - 157

EP - 176

JO - Journal d'Analyse Mathematique

JF - Journal d'Analyse Mathematique

ER -

A minimal area problem in conformal mapping

Abstract

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