minimal surface

Among the surfacesF(x,y,z)=0,  with F twice continuously differentiable, a minimal surfaceMathworldPlanetmathPlanetmath is such that in every of its points, the mean curvatureMathworldPlanetmathPlanetmathPlanetmath vanishes.  Because the mean curvature is the arithmetic meanMathworldPlanetmath of the principal curvaturesMathworldPlanetmathPlanetmath ϰ1 and ϰ2, the equation


is valid in each point of a minimal surface.

A minimal surface has also the property that every sufficiently little portion of it has smaller area than any other regular surface with the same boundary curve.

Trivially, a plane is a minimal surface.  The catenoidMathworldPlanetmath is the only surface of revolution which is also a minimal surface.

Title minimal surface
Canonical name MinimalSurface
Date of creation 2013-03-22 18:08:56
Last modified on 2013-03-22 18:08:56
Owner pahio (2872)
Last modified by pahio (2872)
Numerical id 5
Author pahio (2872)
Entry type Definition
Classification msc 53A05
Classification msc 26B05
Classification msc 26A24
Related topic PlateausProblem
Related topic LeastSurfaceOfRevolution