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.
- U. Dierkes, S. Hildebrandt, A. Küster, O. Wohlrab: Minimal Surfaces
I+II, Grundlehren der Mathematik, Springer Verlag (1992).
- J.C.C. Nitsche: Lectures on Minimal Surfaces I, Cambridge University
- Robert Osserman: A Survey of Minimal Surfaces, Dover Publications New York
As a guide, meshes should have no holes, no degenerate triangles and
elements, no duplicate vertices. Surfaces should have meshes with an adjacency