Compact spacelike hypersurfaces with constant mean curvature in the anti de Sitter space.
New characterizations of linear Weingarten hypersurfaces immersed in the hyperbolic space
In this paper, we deal with complete linear Weingarten hypersurfaces immersed in the hyperbolic space , that is, complete hypersurfaces of whose mean curvature and normalized scalar curvature satisfy for some , . In this setting, under appropriate restrictions on the mean curvature and on the norm of the traceless part of the second fundamental form, we prove that such a hypersurface must be either totally umbilical or isometric to a hyperbolic cylinder of . Furthermore, a rigidity result...
On the quadric CMC spacelike hypersurfaces in Lorentzian space forms
We deal with complete spacelike hypersurfaces immersed with constant mean curvature in a Lorentzian space form. Under the assumption that the support functions with respect to a fixed nonzero vector are linearly related, we prove that such a hypersurface must be either totally umbilical or isometric to a hyperbolic cylinder of the ambient space.
Bernstein type properties of two-sided hypersurfaces immersed in a Killing warped product
Our purpose is to apply suitable maximum principles in order to obtain Bernstein type properties for two-sided hypersurfaces immersed with constant mean curvature in a Killing warped product , whose curvature of the base Mⁿ satisfies certain constraints and whose warping function ρ is concave on Mⁿ. For this, we study situations in which these hypersurfaces are supposed to be either parabolic, stochastically complete or, in a more general setting, L¹-Liouville. Rigidity results related to entire...
On complete linear Weingarten hypersurfaces in locally symmetric Riemannian manifolds
Our aim is to apply suitable generalized maximum principles in order to obtain characterization results concerning complete linear Weingarten hypersurfaces immersed in a locally symmetric Riemannian manifold, whose sectional curvature is supposed to obey standard constraints. In this setting, we establish sufficient conditions to guarantee that such a hypersurface must be either totally umbilical or an isoparametric hypersurface with two distinct principal curvatures one of which is simple.
Parabolicity and rigidity of spacelike hypersurfaces immersed in a Lorentzian Killing warped product
In this paper, we extend a technique due to Romero et al. establishing sufficient conditions to guarantee the parabolicity of complete spacelike hypersurfaces immersed into a Lorentzian Killing warped product whose Riemannian base has parabolic universal Riemannian covering. As applications, we obtain rigidity results concerning these hypersurfaces. A particular study of entire Killing graphs is also made.
Conformal Killing graphs in foliated Riemannian spaces with density: rigidity and stability
In this paper we investigate the geometry of conformal Killing graphs in a Riemannian manifold endowed with a weight function and having a closed conformal Killing vector field with conformal factor , that is, graphs constructed through the flow generated by and which are defined over an integral leaf of the foliation orthogonal to . For such graphs, we establish some rigidity results under appropriate constraints on the -mean curvature. Afterwards, we obtain some stability results...
Sharp eigenvalue estimates of closed -hypersurfaces in locally symmetric spaces
The purpose of this article is to obtain sharp estimates for the first eigenvalue of the stability operator of constant mean curvature closed hypersurfaces immersed into locally symmetric Riemannian spaces satisfying suitable curvature conditions (which includes, in particular, a Riemannian space with constant sectional curvature). As an application, we derive a nonexistence result concerning strongly stable hypersurfaces in these ambient spaces.
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