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Compact Riemann Surfaces

An Introduction to Contemporary Mathematics

  • Textbook
  • © 1997

Overview

Authors:
  1. Jürgen Jost

    1. Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany

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Part of the book series: Universitext (UTX)

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Table of contents (5 chapters)

  1. Front Matter

    Pages I-XIV
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  2. Topological Foundations

    • Jürgen Jost
    Pages 1-17

  3. Differential Geometry of Riemann Surfaces

    • Jürgen Jost
    Pages 19-77

  4. Harmonic Maps

    • Jürgen Jost
    Pages 79-166

  5. Teichmüller Spaces

    • Jürgen Jost
    Pages 167-202

  6. Geometric Structures on Riemann Surfaces

    • Jürgen Jost
    Pages 203-280

  7. Back Matter

    Pages 281-295
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Keywords

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.

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)

Authors and Affiliations

  • Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany

    Jürgen Jost

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

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1997

  • eBook ISBN: 978-3-662-03446-0Published: 17 April 2013

  • Series ISSN: 0172-5939

  • Series E-ISSN: 2191-6675

  • Edition Number: 1

  • Number of Pages: XIV, 295

  • Topics: Differential Geometry

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