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Product Code:  MMONO/26 
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Softcover ISBN:  9780821815762 
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Product Code:  MMONO/26.B 
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Softcover ISBN:  9780821815762 
Product Code:  MMONO/26 
List Price:  $165.00 
MAA Member Price:  $148.50 
AMS Member Price:  $132.00 
eBook ISBN:  9781470444433 
Product Code:  MMONO/26.E 
List Price:  $155.00 
MAA Member Price:  $139.50 
AMS Member Price:  $124.00 
Softcover ISBN:  9780821815762 
eBook ISBN:  9781470444433 
Product Code:  MMONO/26.B 
List Price:  $320.00 $242.50 
MAA Member Price:  $288.00 $218.25 
AMS Member Price:  $256.00 $194.00 

Book DetailsTranslations of Mathematical MonographsVolume: 26; 1969; 676 ppMSC: Primary 30
This book is based on lectures on geometric function theory given by the author at Leningrad State University. It studies univalent conformal mapping of simply and multiply connected domains, conformal mapping of multiply connected domains onto a disk, applications of conformal mapping to the study of interior and boundary properties of analytic functions, and general questions of a geometric nature dealing with analytic functions. The second Russian edition upon which this English translation is based differs from the first mainly in the expansion of two chapters and in the addition of a long survey of more recent developments. The book is intended for readers who are already familiar with the basics of the theory of functions of one complex variable.

Table of Contents

Chapters

A note on the author

Preface to the second edition

Preface (to the first edition)

Introductory geometric considerations

The convergence of sequences of analytic and harmonic functions

The principles of conformal mapping of simply connected domains

Realization of conformal mapping of simply connected domains

Extremal questions and inequalities holding in classes of univalent functions

Univalent conformal mapping of multiply connected domains

Mapping of multiply connected domains onto a disk

The measure properties of closed sets in the plane

Majorization principles and their applications

Boundary value problems for analytic functions defined on a disk

Boundary questions for functions that are analytic inside a rectifiable contour

Some supplementary information


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This book is based on lectures on geometric function theory given by the author at Leningrad State University. It studies univalent conformal mapping of simply and multiply connected domains, conformal mapping of multiply connected domains onto a disk, applications of conformal mapping to the study of interior and boundary properties of analytic functions, and general questions of a geometric nature dealing with analytic functions. The second Russian edition upon which this English translation is based differs from the first mainly in the expansion of two chapters and in the addition of a long survey of more recent developments. The book is intended for readers who are already familiar with the basics of the theory of functions of one complex variable.

Chapters

A note on the author

Preface to the second edition

Preface (to the first edition)

Introductory geometric considerations

The convergence of sequences of analytic and harmonic functions

The principles of conformal mapping of simply connected domains

Realization of conformal mapping of simply connected domains

Extremal questions and inequalities holding in classes of univalent functions

Univalent conformal mapping of multiply connected domains

Mapping of multiply connected domains onto a disk

The measure properties of closed sets in the plane

Majorization principles and their applications

Boundary value problems for analytic functions defined on a disk

Boundary questions for functions that are analytic inside a rectifiable contour

Some supplementary information