Complete Hypersurfaces with Bounded Mean Curvature in ${\mathbb R}^{n+1}$

Hypersurfaces with Constant Mean Curvature in a Lorentzian Space Form

hypersurfaces with constant mean curvature in a lorentzian space form

Complete spacelike hypersurfaces with positive r-th mean curvature in a semi-Riemannian warped product

In this paper, by supposing a natural comparison inequality on the positive r-th mean curvatures of the hypersurface, we obtain some new Bernstein-type theorems for complete spacelike hypersurfaces immersed in a semi-Riemannian warped product of constant sectional curvature. Generalizing the above results, under a restriction on the sectional curvature or the Ricci curvature tensor of the fiber...

Constant mean curvature hypersurfaces foliated by spheres ∗

We ask when a constant mean curvature n-submanifold foliated by spheres in one of the Euclidean, hyperbolic and Lorentz–Minkowski spaces (En+1, Hn+1 or Ln+1), is a hypersurface of revolution. In En+1 and Ln+1 we will assume that the spheres lie in parallel hyperplanes and in the case of hyperbolic space Hn+1, the spheres will be contained in parallel horospheres. Finally, Riemann examples in L3...

Stability of Hypersurfaces with Constant R-th Anisotropic Mean Curvature

Given a positive function F on S which satisfies a convexity condition, we define the r-th anisotropic mean curvature function H r for hypersurfaces in R n+1 which is a generalization of the usual r-th mean curvature function. Let X : M → R be an n-dimensional closed hypersurface with H r+1 =constant, for some r with 0 ≤ r ≤ n− 1, which is a critical point for a variational problem. We show tha...