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 .
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
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
n+1] with vanishing mean curvature
is called maximal.
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).