Complex analysis : conformal inequalities and the Bieberbach conjecture / Prem K. Kythe

Includes bibliographical references and index.

Preface -- Notations Definitions and Acronyms -- 1. Analytic Functions -- 2. Univalent Functions -- 3. Area Principle -- 4.Löwner Theory -- 5.Higher-Order Coefficients -- 6. Subclasses of Univalent Functions -- 7. Generalized Convexity -- 8.Coefficients Estimates -- 9. Polynomials -- 10. De Branges Theorem -- 11. Epilogue: After de Branges -- A Mappings -- B Parametrized Curves -- C Green's Theorems -- D Two-Dimensional Potential Flows -- E Subordination Principle -- Bibliography -- Index

This book 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 and differential equations, the book is suitable for graduate students engaged in analytical research on the topics and researchers working on related areas of complex analysis in one or more complex variables.