Scherk surface

Animation of Scherk's first and second surface transforming into each other: they are members of the same associate family of minimal surfaces.

In mathematics, a Scherk surface (named after Heinrich Scherk) is an example of a minimal surface. Scherk described two complete embedded minimal surfaces in 1834;[1] his first surface is a doubly periodic surface, his second surface is singly periodic. They were the third non-trivial examples of minimal surfaces (the first two were the catenoid and helicoid).[2] The two surfaces are conjugates of each other.

Scherk surfaces arise in the study of certain limiting minimal surface problems and in the study of harmonic diffeomorphisms of hyperbolic space.

  1. ^ H.F. Scherk, Bemerkungen über die kleinste Fläche innerhalb gegebener Grenzen, Journal für die reine und angewandte Mathematik, Volume 13 (1835) pp. 185–208 [1]
  2. ^ "Heinrich Scherk - Biography".