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.
Read more about this topic: Minimal Surface
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