What is "minimal surface"

n. 1 (context mathematics English) Any surface that has the least possible surface area of those into which it could transform; typically the shapes of soap bubbles that span wire frames 2 (context mathematics English) Any surface of vanishing mean curvature. Includes, but is not restricted to, surfaces of minimal area, as given by some boundary conditions.

In mathematics, a minimal surface is a surface that locally minimizes its area. This is equivalent to (see definitions below) having a mean curvature of zero.

The term "minimal surface" is used because these surfaces originally arose as surfaces that minimized total surface area subject to some constraint. Physical models of area-minimizing minimal surfaces can be made by dipping a wire frame into a soap solution, forming a soap film, which is a minimal surface whose boundary is the wire frame. However the term is used for more general surfaces that may self-intersect or do not have constraints. For a given constraint there may also exist several minimal surfaces with different areas (for example, see minimal surface of revolution): the standard definitions only relate to a local optimum, not a global optimum.