Minimal Surfaces I

Boundary Value Problems

  • Ulrich Dierkes
  • Stefan Hildebrandt
  • Albrecht Küster
  • Ortwin Wohlrab

Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 295)

Table of contents

  1. Front Matter
    Pages N4-XIII
  2. Introduction

    1. Ulrich Dierkes, Stefan Hildebrandt, Albrecht Küster, Ortwin Wohlrab
      Pages 1-4
  3. Introduction to the Geometry of Surfaces and to Minimal Surfaces

    1. Front Matter
      Pages 5-5
    2. Ulrich Dierkes, Stefan Hildebrandt, Albrecht Küster, Ortwin Wohlrab
      Pages 6-52
    3. Ulrich Dierkes, Stefan Hildebrandt, Albrecht Küster, Ortwin Wohlrab
      Pages 53-88
    4. Ulrich Dierkes, Stefan Hildebrandt, Albrecht Küster, Ortwin Wohlrab
      Pages 89-217
  4. Plateau’s Problem and Free Boundary Problems

    1. Front Matter
      Pages 219-219
    2. Ulrich Dierkes, Stefan Hildebrandt, Albrecht Küster, Ortwin Wohlrab
      Pages 221-302
    3. Ulrich Dierkes, Stefan Hildebrandt, Albrecht Küster, Ortwin Wohlrab
      Pages 303-366
    4. Ulrich Dierkes, Stefan Hildebrandt, Albrecht Küster, Ortwin Wohlrab
      Pages 367-426
  5. Back Matter
    Pages 427-508

About this book

Introduction

Minimal surfaces I is an introduction to the field of minimal surfaces and apresentation of the classical theory as well as of parts of the modern development centered around boundary value problems. Part II deals with the boundary behaviour of minimal surfaces. Part I is particularly apt for students who want to enter this interesting area of analysis and differential geometry which during the last 25 years of mathematical research has been very active and productive. Surveys of various subareas will lead the student to the current frontiers of knowledge and can alsobe useful to the researcher. The lecturer can easily base courses of one or two semesters on differential geometry on Vol. 1, as many topics are worked out in great detail. Numerous computer-generated illustrations of old and new minimal surfaces are included to support intuition and imagination. Part 2 leads the reader up to the regularity theory fornonlinear elliptic boundary value problems illustrated by a particular and fascinating topic. There is no comparably comprehensive treatment of the problem of boundary regularity of minimal surfaces available in book form. This long-awaited book is a timely and welcome addition to the mathematical literature.

Keywords

Analysis Calculus of Variations Minimal Surfaces Minimal surface Nonlinear Boundary Value Problems Partial Differential Equations differential geometry

Authors and affiliations

  • Ulrich Dierkes
    • 1
  • Stefan Hildebrandt
    • 1
  • Albrecht Küster
    • 1
  • Ortwin Wohlrab
    • 2
  1. 1.Mathematisches InstitutUniversität BonnBonnFederal Republic of Germany
  2. 2.BonnFederal Republic of Germany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-02791-2
  • Copyright Information Springer-Verlag Berlin Heidelberg 1992
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-662-02793-6
  • Online ISBN 978-3-662-02791-2
  • Series Print ISSN 0072-7830
  • Series Online ISSN 2196-9701
  • About this book