Constant mean curvature $k$-noids in homogeneous manifolds

CONSTANT MEAN CURVATURE n-NOIDS WITH PLATONIC SYMMETRIES

Constant k-curvature hypersurfaces in Riemannian manifolds

In [8], Rugang Ye proved the existence of a family of constant mean curvature hypersurfaces in an m+ 1-dimensional Riemannian manifold (M, g), which concentrate at a point p0 (which is required to be a nondegenerate critical point of the scalar curvature), moreover he proved that this family constitute a foliation of a neighborhood of p0. In this paper we extend this result to the other curvatu...

Complete k-Curvature Homogeneous Pseudo-Riemannian Manifolds

For k 2, we exhibit complete k-curvature homogeneous neutral signature pseudoRiemannian manifolds which are not locally affine homogeneous (and hence not locally homogeneous). All the local scalar Weyl invariants of these manifolds vanish. These manifolds are Ricci flat, Osserman, and Ivanov–Petrova. Mathematics Subject Classification (2000): 53B20.

Stable constant mean curvature hypersurfaces in some Riemannian manifolds

We determine all stable constant mean curvature hypersurfaces in a wide class of complete Riemannian manifolds having a foliation whose leaves are umbilical hypersurfaces. Among the consequences of this analysis we obtain all the stable constant mean curvature hypersurfaces in many nonsimply connected hyperbolic space forms. Mathematics Subject Classification (1991). Primary 53A10; Secondary 49...

Hypersurfaces with Constant Mean Curvature in a Lorentzian Space Form