Stable Minimal- and H-Surfaces

  • Ulrich DierkesEmail author
  • Stefan Hildebrandt
  • Friedrich Sauvigny
Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 339)


The principal topic in this chapter is the study of stable minimal surfaces and of stable surfaces of prescribed mean curvature (H-surfaces). In this context it is important to investigate the Gauss map of such a map and its relation to stability. One is led to Bernstein-type results, to Nitsche’s uniqueness theorem, and to the finiteness of the number of minimizers proved by F. Tomi. Furthermore, the above results will enable us in Chapter 7 to solve the nonparametric equation of prescribed mean curvature via the solution of Plateau’s problem for parametric surfaces of prescribed mean curvature. Using and extending the ideas presented in Chapter 4, this more general Plateau problem for H-surfaces will be solved in Vol. 2, Chapter 4.


Minimal Surface Branch Point Principal Curvature Jordan Curve Total Curvature 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Ulrich Dierkes
    • 1
    Email author
  • Stefan Hildebrandt
    • 2
  • Friedrich Sauvigny
    • 3
  1. 1.Faculty of MathematicsUniversity of Duisburg-Essen, Campus DuisburgDuisburgGermany
  2. 2.Mathematical InstituteUniversity of BonnBonnGermany
  3. 3.Mathematical InstituteBrandenburgian Technical UniversityCottbusGermany

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