Minimal Surfaces II

1. Front Matter

   Pages N2-XVI

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2. Introduction

   1. Introduction

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

      Pages 1-3

3. Boundary Behaviour of Minimal Surfaces

   1. Front Matter

      Pages 5-5

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   2. The Boundary Regularity of Minimal Surfaces

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

      Pages 6-140

   3. Singular Boundary Points of Minimal Surfaces

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

      Pages 141-197

   4. Minimal Surfaces with Supporting Half-Planes

      • 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

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   2. The Thread Problem

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

      Pages 250-292

   3. The General Problem of Plateau

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

      Pages 293-340

5. Back Matter

   Pages 341-422

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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.

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

• 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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