Authors:
- Presents a unified and competitive approach to compact and noncompact Riemann surfaces
- Includes continuing exercises that run throughout the book and lead to generalizations of the main theorems
- Will help expand and reinforce a student’s knowledge of analysis, geometry, and topology
- Includes supplementary material: sn.pub/extras
Part of the book series: Cornerstones (COR)
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Table of contents (11 chapters)
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Front Matter
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Analysis on Riemann Surfaces
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Front Matter
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Further Topics
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Front Matter
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Background Material
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Front Matter
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Back Matter
About this book
This textbook presents a unified approach to compact and noncompact Riemann surfaces from the point of view of the so-called L2 $\bar{\delta}$-method. This method is a powerful technique from the theory of several complex variables, and provides for a unique approach to the fundamentally different characteristics of compact and noncompact Riemann surfaces.
The inclusion of continuing exercises running throughout the book, which lead to generalizations of the main theorems, as well as the exercises included in each chapter make this text ideal for a one- or two-semester graduate course. The prerequisites are a working knowledge of standard topics in graduate level real and complex analysis, and some familiarity of manifolds and differential forms.
Reviews
From the reviews:
“The present book gives a solid introduction to the theory of both compact and non-compact Riemann surfaces. While modern introductions often take the view point of algebraic geometry, the present book tries to also cover the analytical aspects. … The book is well written and constitutes a nice contribution to the existing literature on this topic.” (G. Teschl, Internationale Mathematische Nachrichten, Issue 225, 2014)
“This book takes the point of view that Riemann surface theory lies at the root of much of modern analysis, and … illustrate some of the interactions of analysis with geometry and topology. … While much of the book is intended for students at the second-year graduate level, Chapters 1 and 2 and Section 5.2 (along with the required background material) could serve as the basis for the complex analytic analysis component of a year-long first-year graduate-level course on real and complex analysis.” (V. V. Chueshev, Zentralblatt MATH, Vol. 1237, 2012)
Authors and Affiliations
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, Department of Mathematics, Lehigh University, Bethlehem, USA
Terrence Napier
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, Deptartment of Mathematics, State University New York at Buffalo, Buffalo, USA
Mohan Ramachandran
Bibliographic Information
Book Title: An Introduction to Riemann Surfaces
Authors: Terrence Napier, Mohan Ramachandran
Series Title: Cornerstones
DOI: https://doi.org/10.1007/978-0-8176-4693-6
Publisher: Birkhäuser Boston, MA
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Science+Business Media, LCC 2012
Hardcover ISBN: 978-0-8176-4692-9Published: 28 September 2011
eBook ISBN: 978-0-8176-4693-6Published: 08 September 2011
Series ISSN: 2197-182X
Series E-ISSN: 2197-1838
Edition Number: 1
Number of Pages: XVII, 560
Number of Illustrations: 42 b/w illustrations
Topics: Several Complex Variables and Analytic Spaces, Global Analysis and Analysis on Manifolds, Analysis