On hypersurfaces with constant $k$-th mean curvature

Hypersurfaces with Constant Mean Curvature in a Lorentzian Space Form

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...

HYPERSURFACES WITH CONSTANT k-TH MEAN CURVATURE IN A LORENTZIAN SPACE FORM

In this paper, we study n(n ≥ 3)-dimensional complete connected and oriented space-like hypersurfaces Mn in an (n+1)-dimensional Lorentzian space form Mn+1 1 (c) with non-zero constant k-th (k < n) mean curvature and two distinct principal curvatures λ and μ. We give some characterizations of Riemannian product H(c1) ×Mn−m(c2) and show that the Riemannian product Hm(c1)×Mn−m(c2) is the only com...

hypersurfaces with constant mean curvature in a lorentzian space form

Constant Mean Curvature Hypersurfaces with Constant Δ-invariant

We completely classify constant mean curvature hypersurfaces (CMC) with constant δ-invariant in the unit 4-sphere S 4 and in the Euclidean 4-space E 4 .