Title
Hyperbolic Geometry from a Local Viewpoint (London Mathematical Society Student Texts, Series Number 68),New
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Written for graduate students, this book presents topics in 2dimensional hyperbolic geometry. The authors begin with rigid motions in the plane which are used as motivation for a full development of hyperbolic geometry in the unit disk. The approach is to define metrics from an infinitesimal point of view; first the density is defined and then the metric via integration. The study of hyperbolic geometry in arbitrary domains requires the concepts of surfaces and covering spaces as well as uniformization and Fuchsian groups. These ideas are developed in the context of what is used later. The authors then provide a detailed discussion of hyperbolic geometry for arbitrary plane domains. New material on hyperbolic and hyperboliclike metrics is presented. These are generalizations of the Kobayashi and Caratheodory metrics for plane domains. The book concludes with applications to holomorphic dynamics including new results and accessible open problems.
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- Q: What topics are covered in 'Hyperbolic Geometry from a Local Viewpoint'? A: This book covers essential topics in 2-dimensional hyperbolic geometry, including rigid motions, hyperbolic metrics, surfaces, covering spaces, uniformization, and Fuchsian groups.
- Q: Who is the intended audience for this book? A: The book is primarily written for graduate students studying mathematics, particularly those interested in geometry and complex analysis.
- Q: What is the format of this book? A: The book is available in a paperback binding, making it convenient for handling and reading.
- Q: How many pages does the book have? A: The book contains a total of 282 pages, providing a comprehensive exploration of hyperbolic geometry.
- Q: When was 'Hyperbolic Geometry from a Local Viewpoint' published? A: The book was published on April 9, 2007.
- Q: Who are the authors of this book? A: The book is authored by Linda Keen.
- Q: Does this book include new material on hyperbolic metrics? A: Yes, the book introduces new material on hyperbolic and hyperbolic-like metrics, which generalize existing concepts for plane domains.
- Q: What are some applications discussed in the book? A: The book concludes with applications to holomorphic dynamics, including new results and accessible open problems related to the subject.
- Q: Is there any prior knowledge required to understand the content? A: A background in graduate-level mathematics, particularly in geometry and analysis, is recommended to fully comprehend the material.
- Q: What makes this book unique in its approach to hyperbolic geometry? A: The authors provide a local viewpoint, defining metrics from an infinitesimal perspective and developing concepts systematically for complex domains.