e, f, g, the Gaussian curvature K, the mean curvature
In this study, mean curvature
is employed to characterize the surfaces to be compared.
Assume that the mean curvature
form is bounded and coclosed.
For readers who have completed their study of linear elliptic differential equations and intend to explore nonlinear ones, Han discusses quasilinear and fully nonlinear equations, focusing on two important nonlinear elliptic differentials closely related to geometry, the mean curvature
equation and the Monge-Ampere equation.
Hopf, a powerful analytic tool which is often used in the theory of minimal or constant mean curvature
The remaining nine parameters are derived from the Mean Curvature
View namely Max Mean curvature
, Max Mean Curvature
Xmm, Max Mean curvature
Ymm, Centroid Xmm, Centroid Ymm, Convexity Ymm, Convexity, Mean I-S, Mean IN-ST, Mean IN-SN.
Our method to get the estimates parallels that of Escobar and Garcia () in the problem of prescribed mean curvature
on the boundary of the ball.
Submanifolds of E[TM] with harmonic mean curvature
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 .
If the mean curvature
H of the affine translation surface r(x, y) in [E.
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.