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© 1997

Compact Riemann Surfaces

An Introduction to Contemporary Mathematics

Textbook

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages I-XIV
  2. Jürgen Jost
    Pages 1-17
  3. Jürgen Jost
    Pages 79-166
  4. Jürgen Jost
    Pages 167-202
  5. Jürgen Jost
    Pages 203-280
  6. Back Matter
    Pages 281-295

About this book

Introduction

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.

Keywords

Calc Riemann surface Riemann surfaces Riemann-Roch Theorem Teichmüller theory algebra algebraic geometry algebraic topology calculus differential geometry harmonic maps hyberbolic geometry hyperbolic geometry partial differential equation topology

Authors and affiliations

  1. 1.Max Planck Institute for Mathematics in the SciencesLeipzigGermany

Bibliographic information

  • Book Title Compact Riemann Surfaces
  • Book Subtitle An Introduction to Contemporary Mathematics
  • Authors Jürgen Jost
  • Series Title Universitext
  • DOI https://doi.org/10.1007/978-3-662-03446-0
  • Copyright Information Springer-Verlag Berlin Heidelberg 1997
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Softcover ISBN 978-3-540-53334-4
  • eBook ISBN 978-3-662-03446-0
  • Series ISSN 0172-5939
  • Series E-ISSN 2191-6675
  • Edition Number 1
  • Number of Pages XIV, 295
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Differential Geometry
  • Buy this book on publisher's site

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)