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H. F. de Lima, M. A. Velásquez (2011)
Archivum Mathematicum
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In this paper we study the -stability of closed hypersurfaces with constant -th mean curvature in Riemannian manifolds of constant sectional curvature. In this setting, we obtain a characterization of the -stable ones through of the analysis of the first eigenvalue of an operator naturally attached to the -th mean curvature.
Mohamed Jleli (2012)
Annales de l’institut Fourier
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In this paper, we explain how the end-to-end construction together with the moduli space theory can be used to produce compact constant mean curvature hypersurfaces with nontrivial topology. For the sake of simplicity, the hypersurfaces we construct have a large group of symmetry but the method can certainly be used to provide many more examples with less symmetries.
Ximin Liu, Hongxia Li (2005)
Commentationes Mathematicae Universitatis Carolinae
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In this paper, by using Cheng-Yau’s self-adjoint operator , we study the complete hypersurfaces in a sphere with constant scalar curvature.
Sebastião Carneiro de Almeida, Fabiano Gustavo Braga Brito (1997)
Annales de la Faculté des sciences de Toulouse : Mathématiques
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Yaning Wang, Ximin Liu (2012)
Archivum Mathematicum
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A new class of -dimensional Lorentz spaces of index is introduced which satisfies some geometric conditions and can be regarded as a generalization of Lorentz space form. Then, the compact space-like hypersurface with constant scalar curvature of this spaces is investigated and a gap theorem for the hypersurface is obtained.