Skip to main content
SpringerLink
Log in
Book cover

Minimal Surfaces I

Boundary Value Problems

  • Book
  • © 1992

Overview

Authors:
  1. Ulrich Dierkes

    1. Mathematisches Institut, Universität Bonn, Bonn, Federal Republic of Germany

    View author publications

    You can also search for this author in PubMed   Google Scholar

  2. Stefan Hildebrandt

    1. Mathematisches Institut, Universität Bonn, Bonn, Federal Republic of Germany

    View author publications

    You can also search for this author in PubMed   Google Scholar

  3. Albrecht Küster

    1. Mathematisches Institut, Universität Bonn, Bonn, Federal Republic of Germany

    View author publications

    You can also search for this author in PubMed   Google Scholar

  4. Ortwin Wohlrab

    1. Bonn, Federal Republic of Germany

    View author publications

    You can also search for this author in PubMed   Google Scholar

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

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 74.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (7 chapters)

  1. Front Matter

    Pages N4-XIII
    Download chapter PDF

  2. Introduction

    1. Introduction

      • 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
      Download chapter PDF

    2. Differential Geometry of Surfaces in Three-Dimensional Euclidean Space

      • Ulrich Dierkes, Stefan Hildebrandt, Albrecht Küster, Ortwin Wohlrab
      Pages 6-52

    3. Minimal Surfaces

      • Ulrich Dierkes, Stefan Hildebrandt, Albrecht Küster, Ortwin Wohlrab
      Pages 53-88

    4. Representation Formulas and Examples of Minimal Surfaces

      • 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
      Download chapter PDF

    2. The Plateau Problem and the Partially Free Boundary Problem for Minimal Surfaces

      • Ulrich Dierkes, Stefan Hildebrandt, Albrecht Küster, Ortwin Wohlrab
      Pages 221-302

    3. Minimal Surfaces with Free Boundaries

      • Ulrich Dierkes, Stefan Hildebrandt, Albrecht Küster, Ortwin Wohlrab
      Pages 303-366

    4. Enclosure Theorems and Isoperimetric Inequalities for Minimal Surfaces with Fixed or Free Boundaries

      • Ulrich Dierkes, Stefan Hildebrandt, Albrecht Küster, Ortwin Wohlrab
      Pages 367-426

  5. Back Matter

    Pages 427-508
    Download chapter PDF
Back to top

Keywords

About this book

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.

Authors and Affiliations

  • Mathematisches Institut, Universität Bonn, Bonn, Federal Republic of Germany

    Ulrich Dierkes, Stefan Hildebrandt, Albrecht Küster

  • Bonn, Federal Republic of Germany

    Ortwin Wohlrab

Bibliographic Information

Publish with us

Policies and ethics

Back to top

Search

Navigation