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Let M be a compact hypersurface with constant mean curvature immersed into the unit Euclidean sphere S n+1 . In this paper we derive a sharp upper bound for the first eigenvalue of the stability… (More)

In (2) Barbosa, do Carmo and Eschenburg characterized the to- tally umbilical spheres as the only weakly stable compact constant mean cur- vature hypersurfaces in the Euclidean sphere Sn+1. In this… (More)

Let Mn be a complete spacelike hypersurface with constant normalized scalar curvature R in the de Sitter Space S1n + 1. Let H the mean curvature and suppose that = (R - 1) > 0 and £ sup H2 £ C,… (More)

We show that a given $x:M^n\to \bar{M}^{n+1}=I\times_{\phi}F^{n}$ closed spacelike hypersurface with constant mean curvature $H$ and warping function $\phi$ satisfying \phi ''\geq \ma\{H\phi'',0\}$… (More)

In this paper we develop general Minkowski-type formulae for compact spacelike hypersurfaces immersed into conformally stationary spacetimes, that is, Lorentzian manifolds admitting a timelike… (More)

AbstractIn this paper, we prove that the only compact two-sided hypersurfaces with constant mean curvature H which are weakly stable in
$$\mathbb{RP}^{n+1}$$ and have constant scalar curvature are… (More)

To each immersed complete space-like hypersurfaceM with constant normalized scalar curvature R in the de Sitter space S nC1 1 , we associate sup H 2 , where H is the mean curvature of M .I t is… (More)

In this paper we consider compact oriented hypersurfaces M with constant mean curvature and two principal curvatures immersed in the Euclidean sphere. In the minimal case, Perdomo (Perdomo 2004) and… (More)

Abstract In this work we obtain a gap theorem for spacelike submanifolds with parallel mean curvature vector in a semi-Riemannian space form.