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The Bieberbach Conjecture
Sheng Gong, Academia Sinica, Bejing, People's Republic of China
A co-publication of the AMS and International Press.

AMS/IP Studies in Advanced Mathematics
1999; 201 pp; softcover
Volume: 12
ISBN-10: 0-8218-2742-1
ISBN-13: 978-0-8218-2742-0
List Price: US$34
Member Price: US$27.20
Order Code: AMSIP/12.S
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Temporarily out of stock.
Expected date of availability is December 1, 2014.

In 1919, Bieberbach posed a seemingly simple conjecture. That "simple" conjecture challenged mathematicians in complex analysis for the following 68 years! In that time, a huge number of papers discussing the conjecture and its related problems were inspired. Finally in 1984, de Branges completed the solution.

In 1989, Professor Gong wrote and published a short book in Chinese, The Bieberbach Conjecture, outlining the history of the related problems and de Branges' proof. The present volume is the English translation of that Chinese edition with modifications by the author. In particular, he includes results related to several complex variables. Open problems and a large number of new mathematical results motivated by the Bieberbach conjecture are included.

Completion of a standard one-year graduate complex analysis course will prepare the reader for understanding the book. It would make a nice supplementary text for a topics course at the advanced undergraduate or graduate level.

Titles in this series are co-published with International Press, Cambridge, MA.


Advanced undergraduates, graduate students, and research mathematicians interested in functions of a complex variable.


"For those wanting to read about the history and resolution of what for many years was the problem in complex analysis, it should prove useful."

-- Bulletin of the LMS

"This book (with a preface by Carol H. FitzGerald) is a concise, readable, and essentially self-contained account of the mathematics that makes up the history of the Bieberbach conjecture."

-- Zentralblatt MATH

Table of Contents

  • Introduction
  • Löwner theory
  • Grunsky inequality
  • De Branges theorem
  • Several complex variable cases
  • References
  • List of symbols
  • Index
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