The Bieberbach Conjecture
The Bieberbach Conjecture

Author: Sheng Gong

Publisher: American Mathematical Soc.

Published: 1999-07-12

Total Pages: 218

ISBN-13: 0821827421

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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.

Complex Analysis
Complex Analysis

Author: Prem K. Kythe

Publisher: CRC Press

Published: 2016-04-19

Total Pages: 365

ISBN-13: 149871899X

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Complex Analysis: Conformal Inequalities and the Bieberbach Conjecture discusses the mathematical analysis created around the Bieberbach conjecture, which is responsible for the development of many beautiful aspects of complex analysis, especially in the geometric-function theory of univalent functions. Assuming basic knowledge of complex analysis

The Bieberbach Conjecture
The Bieberbach Conjecture

Author: Albert Baernstein (II)

Publisher: American Mathematical Society(RI)

Published: 2014-05-22

Total Pages: 238

ISBN-13: 9781470412487

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Louis de Branges of Purdue University is recognized as the mathematician who proved Bieberbach's conjecture. This book offers insight into the nature of the conjecture, its history and its proof. It is suitable for research mathematicians and analysts.

Univalent Functions
Univalent Functions

Author: Derek K. Thomas

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2018-04-09

Total Pages: 268

ISBN-13: 3110560968

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The study of univalent functions dates back to the early years of the 20th century, and is one of the most popular research areas in complex analysis. This book is directed at introducing and bringing up to date current research in the area of univalent functions, with an emphasis on the important subclasses, thus providing an accessible resource suitable for both beginning and experienced researchers. Contents Univalent Functions – the Elementary Theory Definitions of Major Subclasses Fundamental Lemmas Starlike and Convex Functions Starlike and Convex Functions of Order α Strongly Starlike and Convex Functions Alpha-Convex Functions Gamma-Starlike Functions Close-to-Convex Functions Bazilevič Functions B1(α) Bazilevič Functions The Class U(λ) Convolutions Meromorphic Univalent Functions Loewner Theory Other Topics Open Problems

My Life and Functions
My Life and Functions

Author: Walter K. Hayman

Publisher: Lulu.com

Published: 2014

Total Pages: 174

ISBN-13: 1326032240

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Early life -- Student days -- Newcastle -- Exeter -- Imperial -- Family life -- York -- London -- Marie -- Appendix A: publications to date -- Appendix B: Ph. D. students -- Index

Harmonic Mappings in the Plane
Harmonic Mappings in the Plane

Author: Peter Duren

Publisher: Cambridge University Press

Published: 2004-03-29

Total Pages: 236

ISBN-13: 9781139451277

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Harmonic mappings in the plane are univalent complex-valued harmonic functions of a complex variable. Conformal mappings are a special case where the real and imaginary parts are conjugate harmonic functions, satisfying the Cauchy-Riemann equations. Harmonic mappings were studied classically by differential geometers because they provide isothermal (or conformal) parameters for minimal surfaces. More recently they have been actively investigated by complex analysts as generalizations of univalent analytic functions, or conformal mappings. Many classical results of geometric function theory extend to harmonic mappings, but basic questions remain unresolved. This book is the first comprehensive account of the theory of planar harmonic mappings, treating both the generalizations of univalent analytic functions and the connections with minimal surfaces. Essentially self-contained, the book contains background material in complex analysis and a full development of the classical theory of minimal surfaces, including the Weierstrass-Enneper representation. It is designed to introduce non-specialists to a beautiful area of complex analysis and geometry.