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.