Displaying similar documents to “Sharp eigenvalue estimates of closed H -hypersurfaces in locally symmetric spaces”

Eigenvalue relationships between Laplacians of constant mean curvature hypersurfaces in 𝕊 n + 1

Bingqing Ma, Guangyue Huang (2013)

Communications in Mathematics

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For compact hypersurfaces with constant mean curvature in the unit sphere, we give a comparison theorem between eigenvalues of the stability operator and that of the Hodge Laplacian on 1-forms. Furthermore, we also establish a comparison theorem between eigenvalues of the stability operator and that of the rough Laplacian.

Hypersurfaces with constant curvature in ℝ n + 1

J. A. Gálvez, A. Martínez (2002)

Banach Center Publications

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We give some optimal estimates of the height, curvature and volume of compact hypersurfaces in ℝ n + 1 with constant curvature bounding a planar closed (n-1)-submanifold.

Hypersurfaces with constant k -th mean curvature in a Lorentzian space form

Shichang Shu (2010)

Archivum Mathematicum

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In this paper, we study n ( n ≥ 3 ) -dimensional complete connected and oriented space-like hypersurfaces M n in an (n+1)-dimensional Lorentzian space form M 1 n + 1 ( c ) with non-zero constant k -th ( k < n ) mean curvature and two distinct principal curvatures λ and μ . We give some characterizations of Riemannian product H m ( c 1 ) × M n - m ( c 2 ) and show that the Riemannian product H m ( c 1 ) × M n - m ( c 2 ) is the only complete connected and oriented space-like hypersurface in M 1 n + 1 ( c ) with constant k -th mean curvature and two distinct principal curvatures, if the multiplicities...

On complete linear Weingarten hypersurfaces in locally symmetric Riemannian manifolds

Cícero P. Aquino, Henrique F. de Lima, Fábio R. dos Santos, Marco Antonio L. Velásquez (2015)

Commentationes Mathematicae Universitatis Carolinae

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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...