In 1916 Bieberach conjectured: If f - a univalent holomorphic function on the unit disk - is a member of S - the set of all such functions where D={z:|z| less than 1} and the normalization conditions f(0)=0 and F(0)=1 are added, then |an| is less than n holds true for n=2,3,...This equality holds if and only if f(z) is the Koebe function z over (1-z)2 or one of its rotations. De Branges proved the conjecture in 1984. In the intervening 68 years, a huge number of papers discussed this conjecture and its related problems. This book was originally published in Chinese and makes the full history of the problem available to anyone who has completed the standard material in a one year graduate complex analysis course.

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Sheng Gong, Academia Sinica, Bejing, People's Republic of China.

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

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

*"About this title" may belong to another edition of this title.*

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