Mean Curvature Surfaces

Surfaces with constant or prescribed mean curvature. The mean curvature H of a smooth surface in R3 is the mean of the two principal curvature values. In contrast to minimal surfaces this section considers surfaces where the mean curvature does not vanish identically.

Physically speaking, small parts of constant mean curvature surfaces minimize surfaces area under a volume constraint. Soap bubbles are classical examples.

References

  1. U. Dierkes, S. Hildebrandt, A. Küster, O. Wohlrab: Minimal Surfaces I+II, Grundlehren der Mathematik, Springer Verlag (1992).

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.