Minimal Surfaces I

1. Front Matter

   Pages N4-XIII

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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

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   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

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   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

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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.

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

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

  Ulrich Dierkes, Stefan Hildebrandt, Albrecht Küster

• Bonn, Federal Republic of Germany

  Ortwin Wohlrab

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