The Schwarz Lemma

Book Details

• Publisher: Dover Publications

• Author: Sean Dineen

• Language: English

• Edition: Reprint

• ISBN: 9780486801209

• Pages: 256

• Cover: Paperback

• Dimensions: 9.1 x 6.2 x 0.7 inches

About the Book

The Schwarz Lemma: A Self-contained Introduction is an accessible and comprehensive guide to one of the simplest yet most important results in complex analysis. Focusing on the rigidity of holomorphic functions, this book is designed to be self-contained, requiring no prior knowledge of intrinsic metrics. It provides a thorough overview of the subject, making it suitable for advanced undergraduates and graduate students in mathematics.

The book is divided into two parts:

• Part 1 introduces key concepts such as holomorphic and subharmonic functions and establishes the Schwarz lemma for plurisubharmonic functions. It covers essential topics like the Poincaré distance, Schwarz-Pick systems of pseudodistances, hyperbolic manifolds, special domains, and pseudometrics based on the complex Green function.

• Part 2 focuses on fixed point theorems and the analytic Radon-Nikodym property, extending the discussion to deeper aspects of complex analysis.

This work is a valuable resource for those looking to understand the Schwarz lemma in the context of complex analysis, offering clear explanations, necessary definitions, and a wide range of applications to further research in the field.