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Computational Approach to Riemann Surfaces

  • Alexander I. Bobenko
  • Christian Klein

Part of the Lecture Notes in Mathematics book series (LNM, volume 2013)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Introduction

    1. Front Matter
      Pages 1-1
    2. Alexander I. Bobenko
      Pages 3-64
  3. Algebraic Curves

    1. Front Matter
      Pages 65-65
    2. Jörg Frauendiener, Christian Klein
      Pages 125-162
  4. Schottky Uniformization

    1. Front Matter
      Pages 163-163
    2. Rubén A. Hidalgo, Mika Seppälä
      Pages 195-209
  5. Discrete Surfaces

    1. Front Matter
      Pages 211-211
    2. Alexander I. Bobenko, Christian Mercat, Markus Schmies
      Pages 213-226
  6. Back Matter
    Pages 255-257

About this book

Introduction

This volume offers a well-structured overview of existent computational approaches to Riemann surfaces and those currently in development. The authors of the contributions represent the groups providing publically available numerical codes in this field. Thus this volume illustrates which software tools are available and how they can be used in practice. In addition examples for solutions to partial differential equations and in surface theory are presented. The intended audience of this book is twofold. It can be used as a textbook for a graduate course in numerics of Riemann surfaces, in which case the standard undergraduate background, i.e., calculus and linear algebra, is required. In particular, no knowledge of the theory of Riemann surfaces is expected; the necessary background in this theory is contained in the Introduction chapter. At the same time, this book is also intended for specialists in geometry and mathematical physics applying the theory of Riemann surfaces in their research. It is the first book on numerics of Riemann surfaces that reflects the progress made in this field during the last decade, and it contains original results. There are a growing number of applications that involve the evaluation of concrete characteristics of models analytically described in terms of Riemann surfaces. Many problem settings and computations in this volume are motivated by such concrete applications in geometry and mathematical physics.

Keywords

30-XX, 65-XX,14-XX Riemann surfaces algebraic curves discrete geometry uniformization

Editors and affiliations

  • Alexander I. Bobenko
    • 1
  • Christian Klein
    • 2
  1. 1.Institute of MathematicsTechnical University of BerlinBerlinGermany
  2. 2.Institut de MathématiquesUniversité de BourgogneDijon CedexFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-17413-1
  • Copyright Information Springer-Verlag Berlin Heidelberg 2011
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-17412-4
  • Online ISBN 978-3-642-17413-1
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site