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.

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).