CMC Surfaces

Smyth Surfaces

Constant mean curvature surfaces in euclidean 3-space

Smyth surfaces are constant mean curvature surfaces with a one-parameter metric symmetry [1]. Also known as Mr and Mrs Bubble, Smyth surfaces come in many shapes and sizes, with varying numbers of legs. A Delaunay can be surgically attached to the head to make cylinders.

One-parameter family of three-legged Smyth surfaces.

References

B. Smyth, A generalization of a theorem of Delaunay on constant mean curvature surfaces, Statistical thermodynamics and differential geometry of microstructured materials (Minneapolis, MN, 1991), IMA Vol. Math. Appl., Springer, New York (1993), 123—130 [1226924].