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Mysteries of Minimal Surfaces

This is a video by Hojoo Lee showing complex analysis meets minimal surfaces. In mathematics, a minimal surface is a surface that locally minimizes its area. This is equivalent to having zero mean curvature.The term “minimal surface” is used because these surfaces originally arose as surfaces that minimized total surface area subject to some constraint.

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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.

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