Minimal surface

<p>In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, a minimal surface is a surface that locally minimizes its area. This is equivalent to having zero <a href="/facts/Mean_curvature/lgdJ9b0k">mean curvature</a> (see definitions below).
</p><p>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 <a href="/facts/Soap_film/JCTzDK23">soap film</a>, which is a minimal surface whose boundary is the wire frame. However, the term is used for more general surfaces that may <a href="/facts/Immersed_submanifold/zcUy3Enk">self-intersect</a> or do not have constraints. For a given constraint there may also exist several minimal surfaces with different areas (for example, see <a href="/facts/Minimal_surface_of_revolution/GNKG9kxJ">minimal surface of revolution</a>): the standard definitions only relate to a <a href="/facts/Local_optimum/f40GlzAw">local optimum</a>, not a <a href="/facts/Global_optimum/ADlgnyzV">global optimum</a>.
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Minimal surface open-in-new

Minimal surface