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Minimal Surfaces II

Boundary Regularity

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

Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 296)

Table of contents

  1. Front Matter
    Pages N2-XVI
  2. Introduction

    1. Ulrich Dierkes, Stefan Hildebrandt, Albrecht Küster, Ortwin Wohlrab
      Pages 1-3
  3. Boundary Behaviour of Minimal Surfaces

    1. Front Matter
      Pages 5-5
    2. Ulrich Dierkes, Stefan Hildebrandt, Albrecht Küster, Ortwin Wohlrab
      Pages 6-140
    3. Ulrich Dierkes, Stefan Hildebrandt, Albrecht Küster, Ortwin Wohlrab
      Pages 141-197
    4. Ulrich Dierkes, Stefan Hildebrandt, Albrecht Küster, Ortwin Wohlrab
      Pages 198-247
  4. Ramifications : The Thread Problem. The General Plateau Problem

    1. Front Matter
      Pages 249-249
    2. Ulrich Dierkes, Stefan Hildebrandt, Albrecht Küster, Ortwin Wohlrab
      Pages 250-292
    3. Ulrich Dierkes, Stefan Hildebrandt, Albrecht Küster, Ortwin Wohlrab
      Pages 293-340
  5. Back Matter
    Pages 341-422

About this book

Introduction

Minimal Surfaces I is an introduction to the field of minimal surfaces and a presentation 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 also be 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 for nonlinear 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

Minimal surface analysis calculus of variations differential geometry minimal surfaces nonlinear boundary value problems partial differential equations

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/10.1007/978-3-662-08776-3
  • Copyright Information Springer-Verlag Berlin Heidelberg 1992
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-662-08778-7
  • Online ISBN 978-3-662-08776-3
  • Series Print ISSN 0072-7830
  • Buy this book on publisher's site