**Translations of Mathematical Monographs**

1969;
676 pp;
Softcover

MSC: Primary 30;

**Print ISBN: 978-0-8218-1576-2
Product Code: MMONO/26**

List Price: $135.00

AMS Member Price: $108.00

MAA Member Price: $121.50

**Electronic ISBN: 978-1-4704-4443-3
Product Code: MMONO/26.E**

List Price: $135.00

AMS Member Price: $108.00

MAA Member Price: $121.50

# Geometric Theory of Functions of a Complex Variable

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*G. M. Goluzin*

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

# Table of Contents

## Geometric Theory of Functions of a Complex Variable

- Cover Cover11
- Title page iii4
- Contents v6
- A note on the author 110
- Preface to the second edition 312
- Preface (to the first edition) 413
- Introductory geometric considerations 514
- The convergence of sequences of analytic and harmonic functions 1120
- The principles of conformal mapping of simply connected domains 2332
- Realization of conformal mapping of simply connected domains 7685
- Extremal questions and inequalities holding in classes of univalent functions 110119
- Univalent conformal mapping of multiply connected domains 205214
- Mapping of multiply connected domains onto a disk 254263
- The measure properties of closed sets in the plane 293302
- Majorization principles and their applications 329338
- Boundary value problems for analytic functions defined on a disk 380389
- Boundary questions for functions that are analytic inside a rectifiable contour 417426
- Some supplementary information 454463
- The scientific works of Gennadii Mihailovic Goluzin 545554
- Bibliography 549558
- Supplement. Methods and results of the geometric theory of functions 563572
- Bibliography for the Supplement 651660
- Subject Index 673682
- Back Cover Back Cover1687