Mean Curvature


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mean curvature

[¦mēn ′kər·və·chər]
(mathematics)
Half the sum of the principal curvatures at a point on a surface.

Mean Curvature

 

The mean curvature of a surface at a given point P on the surface is equal to the average of the principal curvatures of the surface at the point (seeDIFFERENTIAL GEOMETRY). If E, F, and G are the coefficients of the first fundamental quadratic form of the surface and L, M, and N are the coefficients of the surface’s second fundamental quadratic form, then the mean curvature H can be computed from the formula

If the mean curvature is equal to zero at every point of the surface, then the surface is known as a minimal surface.

References in periodicals archive ?
do Carmo: Hypersurfaces with constant mean curvature in sphere, Proc.
The main extrinsic invariant is the squared mean curvature and the main intrinsic invariants include the classical curvature invariants, namely the scalar curvature and the Ricci curvature; and the well known modern curvature invariant, namely Chen invariant [2].
Similarly, the function H : M [right arrow] R, H(P) = traceS(P)/dim M is called the mean curvature of M at point P.
One should keep in mind that the length of a fiber (with small cross-section) is approximately proportional to the integral of the mean curvature of the fiber.
Five lectures cover geometric partial differential equations in the presence of isolated singularities, constant mean curvature surfaces in metric Lie groups, stochastic methods for minimal surfaces, the role of minimal surfaces in the study of the Allen-Cahn equation, and curvature estimates for constant mean curvature surfaces.
3 software to derive several land-surface models from the initial DEM: slopes model, mean curvature model, maximum curvature model, minimum curvature model and runoff model.
By means of Tr(h), we define the mean curvature vector H of M by
A sampling of more detailed topics turns up functional analysis, symmetric hyperbolic systems, characterizations of global hyperbolicity, local existence, constant mean curvature, and asymptotic behavior.
3] with nonvanishing mean curvature, which describes these surfaces in terms of their Gauss maps and mean curvature functions.
The Significance of Average mean curvature and its determination by quantitative metallography.
eq] denotes the mean curvature of the LV interface at equilibrium (which may take on either positive or negative values).

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