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Minimal Surfaces with Free Boundaries

  • Ulrich DierkesEmail author
  • Stefan Hildebrandt
  • Anthony J. Tromba
Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 340)

Abstract

This chapter is centered on the proof of existence theorems for minimal surfaces with completely free boundaries. The problem is approached by applying the direct methods of the calculus of variations, thus establishing the existence of minimizers with a boundary on a given supporting surface S. However, this method does not yield the existence of stationary minimal surfaces which are not area minimizing. The remaining part of the chapter deals with additional properties of minimal surfaces with free boundaries. For instance, such a surface has to intersect the free boundary surface perpendicularly and in a balanced way. This fact implies nonexistence in certain cases. Finally an extensive report on the existence of stationary minimal surfaces with free or partially free boundaries is given.

Keywords

Free Boundary Minimal Surface Branch Point Convex Body Homotopy Class 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Ulrich Dierkes
    • 1
    Email author
  • Stefan Hildebrandt
    • 2
  • Anthony J. Tromba
    • 3
  1. 1.Fakultät für MathematikUniversität Duisburg-Essen, Campus DuisburgDuisburgGermany
  2. 2.Mathematical InstituteUniversity of BonnBonnGermany
  3. 3.Department of MathematicsUniversity of California at Santa CruzSanta CruzUSA

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