page_title: Scherk surface
section_title: Construction of a simple Scherk surface
hierarchical_section_title: Scherk surface / Scherk's first surface / Construction of a simple Scherk surface
caption_attribution_description: Superficie di Scherk, superficie minima di traslazione
context_page_description: In mathematics, a Scherk surface is an example of a minimal surface. Scherk described two complete embedded minimal surfaces in 1834; 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 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.
context_section_description: Consider the following minimal surface problem on a square in the Euclidean plane: for a natural number n, find a minimal surface Σₙ as the graph of some function
  such that
  That is, uₙ satisfies the minimal surface equation
  and
  What, if anything, is the limiting surface as n tends to infinity? The answer was given by H. Scherk in 1834: the limiting surface Σ is the graph of
  That is, the Scherk surface over the square is
caption: Nine periods of the Scherk surface.
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