Karl Jones: Created page with "In mathematics, a '''minimal surface''' is a surface that locally minimizes its area. This is equivalent to having a mean curvature of zero. == Description == The te..."

2016-10-13T02:05:18Z

Created page with "In mathematics, a '''minimal surface''' is a surface that locally minimizes its area. This is equivalent to having a mean curvature of zero. == Description == The te..."

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In [[mathematics]], a '''minimal surface''' is a surface that locally minimizes its area. This is equivalent to having a [[mean curvature]] of zero.

== Description ==

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 [[Maxima and minima|global optimum]].

== See also ==

* [[Bernstein's problem]]
* [[Bilinear interpolation]]
* [[Bryant surface]]
* [[Curvature]]
* [[Enneper–Weierstrass parameterization]]
* [[Harmonic map]]
* [[Harmonic morphism]]
* [[Patterns in nature]]
* [[Plateau's problem]]
* [[Schwarz minimal surface]]
* [[Soap bubble]]
* [[Surface Evolver]]
* [[Stretched grid method]]
* [[Tensile structure]]
* [[Triply periodic minimal surface]]
* [[Weaire–Phelan structure]]

== External links ==

* [https://en.wikipedia.org/wiki/Minimal_surface Minimal surface] @ Wikipedia

[[Category:Mathematics]]

Minimal surface - Revision history

Karl Jones: Created page with "In mathematics, a '''minimal surface''' is a surface that locally minimizes its area. This is equivalent to having a mean curvature of zero. == Description == The te..."