Convex and Starlike Mappings in Several Complex Variables: 435 (Mathematics and Its Applications) - Softcover

Sheng Gong, Sheng

Softcover

ISBN 10: 9401061912 ISBN 13: 9789401061919

Verlag: Springer, 2012

Inhaltsangabe

This book deals with the theory of convex and starlike biholomorphic mappings in several complex variables. The underlying theme is the extension to several complex variables of geometric aspects of the classical theory of univalent functions. This is the first book which systematically studies this topic. It gathers together, and presents in a unified manner, the current state of affairs for convex and starlike biholomorphic mappings in several complex variables. The majority of the results presented are due to the author, his co-workers and his students.
Audience: This volume will be of interest to research mathematicians whose work involves several complex variables and one complex variable.

Über diesen Titel

Reseña del editor

This interesting book deals with the theory of convex and starlike biholomorphic mappings in several complex variables. The underly­ ing theme is the extension to several complex variables of geometric aspects of the classical theory of univalent functions. Because the author's introduction provides an excellent overview of the content of the book, I will not duplicate the effort here. Rather, I will place the book into historical context. The theory of univalent functions long has been an important part of the study of holomorphic functions of one complex variable. The roots of the subject go back to the famous Riemann Mapping Theorem which asserts that a simply connected region n which is a proper subset of the complex plane C is biholomorphically equivalent to the open unit disk ~. That is, there is a univalent function (holo­ morphic bijection) I : ~ -+ n. In the early part of this century work began to focus on the class S of normalized (f (0) = 0 and I' (0) = 1) univalent functions defined on the unit disk. The restriction to uni­ valent functions defined on the unit disk is justified by the Riemann Mapping Theorem. The subject contains many beautiful results that were obtained by fundamental techniques developed by many mathe­ maticians, including Koebe, Bieberbach, Loewner, Goluzin, Grunsky, and Schiffer. The best-known aspect of univalent function theory is the so-called Bieberbach conjecture which was proved by de Branges in 1984.

Details zur Ausgabe

• Verlag: Springer
• Erscheinungsdatum: 2012
• ISBN 10: 9401061912
• ISBN 13: 9789401061919
• Einband: Tapa blanda
• Sprache: Englisch
• Anzahl der Seiten: 228
• Kontakt zum Hersteller: Nicht verfügbar