Overview
- It is unique among textbooks on Riemann surfaces in including an introduction to Teichmüller theory
- The analytic approach is likewise new as it is based on the theory of harmonic maps
- Includes supplementary material: sn.pub/extras
Part of the book series: Universitext (UTX)
Access this book
We’re sorry, something doesn't seem to be working properly.
Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.
Other ways to access
About this book
Although Riemann surfaces are a time-honoured field, this book is novel in its broad perspective that systematically explores the connection with other fields of mathematics. It can serve as an introduction to contemporary mathematics as a whole as it develops background material from algebraic topology, differential geometry, the calculus of variations, elliptic PDE, and algebraic geometry. It is unique among textbooks on Riemann surfaces in including an introduction to Teichmüller theory. The analytic approach is likewise new as it is based on the theory of harmonic maps. For this new edition, the author has expanded and rewritten several sections to include additional material and to improve the presentation.
Similar content being viewed by others
Keywords
Table of contents (6 chapters)
Reviews
From the reviews:
"Compact Riemann Surfaces: An Introduction to Contemporary Mathematics starts off with a wonderful Preface containing a good deal of history, as well as Jost’s explicit dictum that there are three foci around which the whole subject revolves … . Jost’s presentation is quite accessible, modulo a lot of diligence on the part of the reader. It’s a very good and useful book, very well-written and thorough." (Michael Berg, MathDL, April, 2007)
From the reviews of the third edition:
“Geometrical facts about Riemann surfaces are as ‘nice’ as possible, and they often provide the intuition and motivation for generalizations to other curves, manifolds or varieties. The Riemann–Roch theorem … is a prime example of this influence. This book is amazing, very well written, accessible and works as a first course on Riemannian Surfaces I recommend to the all readers interested in Geometry and Riemannian Geometry.” (Philosophy, Religion and Science Book Reviews, bookinspections.wordpress.com, July, 2013)
Authors and Affiliations
Bibliographic Information
Book Title: Compact Riemann Surfaces
Book Subtitle: An Introduction to Contemporary Mathematics
Authors: Jürgen Jost
Series Title: Universitext
DOI: https://doi.org/10.1007/978-3-540-33067-7
Publisher: Springer Berlin, Heidelberg
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2006
Softcover ISBN: 978-3-540-33065-3Published: 19 June 2006
eBook ISBN: 978-3-540-33067-7Published: 13 December 2006
Series ISSN: 0172-5939
Series E-ISSN: 2191-6675
Edition Number: 3
Number of Pages: XVIII, 282
Number of Illustrations: 23 b/w illustrations
Topics: Differential Geometry