minimal surface
Among the surfaces , with twice continuously differentiable, a minimal surface is such that in every of its points, the mean curvature vanishes. Because the mean curvature is the arithmetic mean of the principal curvatures and , 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 catenoid is the only surface of revolution which is also a minimal surface.
Title | minimal surface |
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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 |