Compact Riemann Surfaces

An Introduction to Contemporary Mathematics

  • Jürgen Jost

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

  • Jürgen Jost
    • 1
  1. 1.Max Planck Institute for Mathematics in the SciencesLeipzigGermany

Bibliographic information

  • 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
  • Print ISBN 978-3-540-53334-4
  • Online ISBN 978-3-662-03446-0
  • Series Print ISSN 0172-5939
  • Series Online ISSN 2191-6675
  • About this book
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