**Mathematical Surveys and Monographs**

Volume: 21;
1986;
218 pp;
Softcover

MSC: Primary 30;

Print ISBN: 978-0-8218-1521-2

Product Code: SURV/21

List Price: $74.00

AMS Member Price: $59.20

MAA Member Price: $66.60

**Electronic ISBN: 978-1-4704-1248-7
Product Code: SURV/21.E**

List Price: $74.00

AMS Member Price: $59.20

MAA Member Price: $66.60

# The Bieberbach Conjecture: Proceedings of the Symposium on the Occasion of the Proof

Share this page *Edited by *
*Albert Baernstein; David Drasin; Peter Duren; Albert Marden*

For over 70 years, the Bieberbach conjecture has intrigued the mathematical
world. Many students of mathematics, who have had a first course in
function theory, have tried their hand at a proof. But many have
invested fruitless years of carefully manipulating inequalities in an
attempt to establish the correct bound.

In 1977, Louis de Branges of Purdue University took up the challenge
of this famous unsolved problem, but in his case the outcome was
different. He will be recognized as the mathematician who proved
Bieberbach's conjecture. And more importantly, his method came from
totally unexpected sources: operator theory and special functions.

This book, based on the Symposium on the Occasion of the Proof, tells the
story behind this fascinating proof and offers insight into the
nature of the conjecture, its history and its proof. A special and
unusual feature of the book is the enlightened personal accounts of the
people involved in the exciting events surrounding the proof. Especially
attractive are the photographs of mathematicians who have made
significant contributions to univalent functions, the area of complex
analysis which provides the setting for the Bieberbach conjecture.

Research mathematicians, especially analysts, are sure to enjoy the
articles in this volume. Most articles require only a basic knowledge
of real and complex analysis. The survey articles are accessible
to non-specialists, and the personal accounts of all who have played
a part in this important discovery will fascinate any reader.

“The remarks by de Branges himself about the discovery of his proof
should be read by all young mathematicians. He describes the
difficulty he had in convincing the experts in the field that a
mathematician, whose work was considered to lie in an entirely
different area, had actually proved a problem of such long standing.
When a mathematician is sure that he has the solution of a problem, he
must persist until he convinces others or is actually proved wrong.”
(Prepublication comments by James A. Hummel, The University of
Maryland, College Park.)

#### Table of Contents

# Table of Contents

## The Bieberbach Conjecture: Proceedings of the Symposium on the Occasion of the Proof

- Contents v8 free
- Preface vii10 free
- List of Contributors xv18 free
- Mathematical Papers 120 free
- Classical analysis: present and future 120
- Inequalities for polynomials 726
- On interpolation, Blaschke products, and balayage of measures 3352
- Powers of Riemann mapping functions 5170
- 300 years of analyticity 6988
- Problems in mathematical physics connectedwith the Bieberbach conjecture 7998
- Extremal methods 85104
- The method of the extremal metric 95114
- Some problems in complex analysis 105124
- Comments on the proof of the conjecture on logarithmic coefficients 109128
- Notes on two function models 113132
- The growth of the derivative of a univalent function 143162
- Shift-invariant subspaces from the Brangesian point of view 153172
- The Cauchy integral, chord-arc curves, and quasiconformal mappings 167186
- Zippers and univalent functions 185204

- Personal Accounts 199218