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Geometric Theory of Functions of a Complex Variable
 
Geometric Theory of Functions of a Complex Variable
Softcover ISBN:  978-0-8218-1576-2
Product Code:  MMONO/26
List Price: $165.00
MAA Member Price: $148.50
AMS Member Price: $132.00
eBook ISBN:  978-1-4704-4443-3
Product Code:  MMONO/26.E
List Price: $155.00
MAA Member Price: $139.50
AMS Member Price: $124.00
Softcover ISBN:  978-0-8218-1576-2
eBook: ISBN:  978-1-4704-4443-3
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
Geometric Theory of Functions of a Complex Variable
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Geometric Theory of Functions of a Complex Variable
Softcover ISBN:  978-0-8218-1576-2
Product Code:  MMONO/26
List Price: $165.00
MAA Member Price: $148.50
AMS Member Price: $132.00
eBook ISBN:  978-1-4704-4443-3
Product Code:  MMONO/26.E
List Price: $155.00
MAA Member Price: $139.50
AMS Member Price: $124.00
Softcover ISBN:  978-0-8218-1576-2
eBook ISBN:  978-1-4704-4443-3
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 Details
     
     
    Translations of Mathematical Monographs
    Volume: 261969; 676 pp
    MSC: 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
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 261969; 676 pp
MSC: 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.

  • 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
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.