Stable space-like hypersurfaces with constant scalar curvature in generalized Roberston-Walker spacetimes

Linear Weingarten hypersurfaces in a unit sphere

In this paper, by modifying Cheng-Yau$'$s technique to complete hypersurfaces in $S^{n+1}(1)$, we prove a rigidity theorem under the hypothesis of the mean curvature and the normalized scalar curvature being linearly related which improve the result of [H. Li, Hypersurfaces with constant scalar curvature in space forms, {em Math. Ann.} {305} (1996), 665--672].  

Hypersurfaces with Constant Mean Curvature in a Lorentzian Space Form

Uniqueness of complete spacelike hypersurfaces in generalized Robertson-Walker spacetimes

In this paper we study the uniqueness of complete noncompact spacelike hypersurfaces immersed in generalized Robertson-Walker (GRW) spacetimes. According to a suitable restriction on the higher order mean curvature and the norm of the gradient of the height function of the hypersurface, we obtain some rigidity theorems in GRW spacetimes. Besides, we establish nonparametric results on the entire...

Uniqueness of Noncompact Spacelike Hypersurfaces of Constant Mean Curvature in Generalized RobertsonWalker Spacetimes

On any spacelike hypersurface of constant mean curvature of a Generalized Robertson–Walker spacetime, the hyperbolic angle y between the future-pointing unit normal vector field and the universal time axis is considered. It is assumed that y has a local maximum. A physical consequence of this fact is that relative speeds between normal and comoving observers do not approach the speed of light n...

‎Spacelike hypersurfaces with constant $S$ or $K$ in de Sitter‎ ‎space or anti-de Sitter space

‎Let $M^n$ be an $n(ngeq 3)$-dimensional complete connected and‎ ‎oriented spacelike hypersurface in a de Sitter space or an anti-de‎ ‎Sitter space‎, ‎$S$ and $K$ be the squared norm of the second‎ ‎fundamental form and Gauss-Kronecker curvature of $M^n$‎. ‎If $S$ or‎ ‎$K$ is constant‎, ‎nonzero and $M^n$ has two distinct principal‎ ‎curvatures one of which is simple‎, ‎we obtain some‎ ‎charact...