Minimal Surface - Examples

Examples

Classical examples of minimal surfaces include:

• the plane, which is a trivial case
• catenoids: minimal surfaces made by rotating a catenary once around its directrix
• helicoids: A surface swept out by a line rotating with uniform velocity around an axis perpendicular to the line and simultaneously moving along the axis with uniform velocity

Surfaces from the 19th century golden age include:

• Schwarz minimal surfaces: triply periodic surfaces that fill R3
• Riemann's minimal surface: A posthumously described periodic surface
• the Enneper surface
• the Hennenberg surface: the first non-orientable minimal surface

Modern surfaces include:

• the Gyroid: One of Schoen's 1970 surfaces, a triply periodic surface of particular interest for liquid crystal structure
• the Saddle tower family: generalisations of Scherk's second surface
• Costa's minimal surface: Famous conjecture disproof. Described 1982 by Celso Costa and later visualized by Jim Hoffman. Jim Hoffman, David Hoffman and William Meeks III then extended the definition to produce a family of surfaces with different rotational symmetries.
• the Chen–Gackstatter surface family, adding handles to the Enneper surface.