Minimal Surfaces

Minimal surfaces in Euclidean 3-space and higher dimensions. The surfaces with vanishing mean curvature H = 0 are called minimal surfaces. The mean curvature H of a smooth surface in R3 is the mean of the two principal curvature values. Locally, such surfaces are shaped like a saddle and minimize surface area.

Minimal surfaces appear in various mathematical disciplines like differential geometry, calculus of variations and partial differential equations, as well as in other sciences like crystallography and chemistry.


  1. U. Dierkes, S. Hildebrandt, A. Küster, O. Wohlrab: Minimal Surfaces I+II, Grundlehren der Mathematik, Springer Verlag (1992).
  2. J.C.C. Nitsche: Lectures on Minimal Surfaces I, Cambridge University Press (1989).
  3. Robert Osserman: A Survey of Minimal Surfaces, Dover Publications New York (1986).

Technical Note

As a guide, meshes should have no holes, no degenerate triangles and elements, no duplicate vertices. Surfaces should have meshes with an adjacency relation.