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Cornerstones

An Introduction to Riemann Surfaces

Authors: Napier, Terrence, Ramachandran, Mohan

  • 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
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eBook $69.99
price for USA (gross)
  • ISBN 978-0-8176-4693-6
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $89.99
price for USA
  • ISBN 978-0-8176-4692-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
About this Textbook

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)


Table of contents (11 chapters)

  • Complex Analysis in ℂ

    Napier, Terrence (et al.)

    Pages 3-23

  • Riemann Surfaces and the L 2 $\bar{\partial}$ -Method for Scalar-Valued Forms

    Napier, Terrence (et al.)

    Pages 25-99

  • The L 2 $$\bar{\partial}$$ -Method in a Holomorphic Line Bundle

    Napier, Terrence (et al.)

    Pages 101-154

  • Compact Riemann Surfaces

    Napier, Terrence (et al.)

    Pages 157-189

  • Uniformization and Embedding of Riemann Surfaces

    Napier, Terrence (et al.)

    Pages 191-309

Buy this book

eBook $69.99
price for USA (gross)
  • ISBN 978-0-8176-4693-6
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $89.99
price for USA
  • ISBN 978-0-8176-4692-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
An Introduction to Riemann Surfaces
Authors
Series Title
Cornerstones
Copyright
2012
Publisher
Birkhäuser Basel
Copyright Holder
Springer Science+Business Media, LCC
eBook ISBN
978-0-8176-4693-6
DOI
10.1007/978-0-8176-4693-6
Hardcover ISBN
978-0-8176-4692-9
Series ISSN
2197-182X
Edition Number
1
Number of Pages
XVII, 560
Number of Illustrations and Tables
42 b/w illustrations
Topics